GB2514110A - Electronic sight tube for visualising multiphase flow in a pipe - Google Patents

Abstract

A system for an electronic sight tube for visualising multiphase and other flows in industrial processes comprises a method and apparatus for monitoring one or more materials flowing in a pipe comprising a monitoring module coupled to the pipe and a calculation module adapted to provide output data representing mass per unit volume of one or more materials or mixtures of materials in the flow over at least a portion of the cross-sectional area of the interior of the pipe by processing at least one variable representing electrical permittivity of the material flowing in the pipe. Preferably the monitoring module comprises a transmitter system adapted to transmit electromagnetic signals and a receiver system adapted to receive electromagnetic signals, the transmitter and receiver systems comprising a plurality of electrodes located at angular positions around the circumference of the pipe; an analyser adapted to determine the difference between the transmitted and received electromagnetic signals; and a calculation module adapted to process the data representing the difference to provide output data representing density of one or more materials or mixtures of materials in the flow, the processing including at least one variable representing electrical permittivity of the mixture of the materials.

Description

3 TITLE: ELECTRONIC SIGHT TUBE FOR VISUALISING 4 MULTIPHASE FLOW IN A PIPE

6 DESCRIPTION

S Background to the invention

In many industrial processes a mixture of fluids, or mixture of fluids and solids is 11 flowing in a pipe. This invention relates to a method of visualising the flows in such 12 processes. Such flows are often at high pressure, high temperature, or contain 13 materials that are chemicafly, biologically or radioactively hazardous. Because of the 14 nature of these flows, or because of other problems such as erosion, corrosion or deposition of solid contaminents they are often conveyed in pipes constructed of steel, 16 iron, other metals, ceramics or plastic wherein the pipe is not transparent and either 17 cannot easily be made transparent or if a transparent section is available the opaque 18 nature of the fluid or mixture of fluids does not allow the internal part of the flow to 19 be seen.

21 Because thc multiphasc flows dcscribcd abovc contain a mixturc of materials, 22 variously gas, liquid, divided solids and combinations thereoL there are a variety of 23 flow regimes or patterns that occur. For example a gas may flow smoothly over the 24 top of a liquid layer in a horizontal pipe, large bubbles may fill the pipe intermittently, slurries or solids may move in waves, or the flow may even plug and stop 26 completely. Many other flow patterns may occur in diverse mixtures. Each of these 27 flow regimes or patterns may have commercially or technically important 28 implications, for example the energy used to transport the fluids may vary with flow 29 regime, the mixing between the phases may be important in the process and will vary with flow regime, it may be important that certain of the phases do not touch the 31 internal surface of the pipe, some flow regimes may lead to more erosion or I deposition than others, and different flow regimes may influence the output from 2 conventional flow sensors in such a way that measurements made of the flow are not 3 correct.

Traditionally in an industrial process where a product is moving in a pipe and where a 6 view of the internal flow is required, a short section of transparent pipe is inserted in 7 the flow line. When the fluids are hot or at high pressure such a sight tube must be 8 enclosed within a secondary structure itself containing transparent sections or 9 windows.

11 Because the exact nature of the flow regime may affect the results, value, cost or 12 management of the industrial process and yet the nature of multiphase flows renders a 13 view into the flow difficult or impossible there is a need in these applications for a 14 method of visualising the internal flow processes without the use of an optical sight tube.

17 A number of physical principles have been used to visualise internal flow processes in 18 industrial pipes or vessels, these are referred to in general as flow imaging or process 19 imaging. Such methods include the measurement of electrical capacitance, electrical conductivity, x-rays, gamma-rays, nuclear magnetic resonance, magnetic fields or 21 nuclconics emission ofparticlcs. Many of these techniques have been applied in 22 research tests and pilot-scale plants but few are in wide-scale use in industrial 23 applications. For example: CN2826373 (Y) discloses image pick-up tracking and 24 detecting system, GB22 12903 (A) describes x-ray stereoscopic imaging system, CN1344929 (A) discloses resistance ehromatographic instrument, CN102410974 (A) 26 discloses pulse laser sources, W020 1203 1292 (Al) discloses ultrasonic scanning, 27 W02012100385 (Al) discloses a gamma ray imaging device, KR100815210 (BI) 28 discloses a 3D particle mage velocity meter, JP20042121 17 (A) discloses X-ray.

29 IJS2OI 1109308 (Al) and 1JS2012174684 (Al) describes magnetic resonance and CN102364046 (A) discloses light intensity modulation type optical fiber sensors, 32 Normally such imaging techniques are used to show a cross-section of the pipe either 33 normal to the flow direction or along the flow direction, and more recent 34 developments have led to 3-dimensional imaging of the body of the flows. For I example: JP2004333237 (A) describes a method to reconfigure the visualization 2 image of a mixed flow in a fluid transport pipe by process tomography and 3 CN2695964 (Y) describes discloses an oil-gas two-phase flow investigating device 4 based-on capacitive chromatographic imaging system.

6 Flow imaging techniques such as ECT (electrical capacitance tomography) have been 7 developed into working flowmeters for certain applications and other of the 8 techniques are used as part of the technology of multiphase flow metering.

9 GB2390683 (B) describes a flow meter based on electrical capacitance tomography wherein image data sets representing concentration arc used to calculate flowratcs of 11 multiphase flows and for example Hunt, Pendleton and Byars in 2004 described in 12 reference [1] a method of estimating volume and mass of solid objects using ECT, 13 while Hunt Pendleton and Ladam in 2004 in reference [2] described measurements of 14 flow structures in mixtures of oil and gas. In all three of these references, as in other publications, the ECT sensors are calibrated so as to measure the fraction of volume 16 that each phase is present in any given volume of the pipe. This fraction is known as 17 volume fraction or holdup.

19 The difficulties of implementing flow or process imaging in industrial applications include the cost -such devices often cost ten times or more the cost of standard flow 21 meters or other sensors; the danger and complexity of implementing nucleonic 22 measurements in standard industrial processes; and the practical difficulty of making 23 complex measurements of this kind in pipes at high pressure and temperature. In 24 addition, knowledge of the volume fraction may not be sufficient or appropriate, a knowledge of the density distribution in the pipe may be more helpful.

27 The present invention relates to a method for estimating the density of the 28 components of a mixture of fluids or a mixture of fluids and solids flowing in a pipe 29 or moving in other closed vessels. Such flows are generically known as multiphase or multicomponent flow. Multiphase flows exist in many industries and examples of 31 such flows include the following applications: 33 1. the flow of mixtures of oil, gas and water in the production of oil and gas; 34 2. gas flows with small amounts of liquid present, often referred to as wet-gas; 3. the flow of water drops and water vapour (known as wet steam) in the power 2 generation industry; 3 4. the flow of powdered coal mixed with air in power generation; 4 5. the flow of thy materials mixed with air in pneumatic conveying; 6. the flow of grain down chutes and tubes in flour milling; 6 7. the flow of grain and other solids moved by gravity through the processes of a 7 flour mill; 8 8. the flow of coal or other combustible material into the burners of a cement 9 manufacturing plant; 9. the flow of dispersed solids moved by augers, conveyors or other mechanical 11 devices; 12 10. the flow of slurries in mining and other industries; 13 II. the flow of combustible solids into biofuel power plants when conveyed by 14 pneumatic or mechanical means.

16 It should be understood that these are merely examples, the invention detailed here is 17 designed to be used with any mixture of fluids and solids being moved in a process by 18 any mechanical, hydraulic or pneumatic means.

Summary of Invention

22 The key embodiment of this invention is a system for an electronic sight tube 23 comprising ofa monitoring module with a plurality of electrodes coupled on to a pipe 24 to visualise multi-phase or other flows.

26 The invention may be used to monitor pipes or other process vessels containing gases, 27 liquids or multiphase mixtures of one or more gases, liquids or solids 29 The invention includes a method and apparatus for monitoring one or more materials flowing in a pipe comprising a monitoring module coupled to the pipe and a 31 calculation module adapted to provide output data representing mass per unit volume 32 of one or more materials or mixtures of materials in the flow over at least a portion of I the cross-sectional area of the interior of the pipe by processing at least one variable 2 representing electrical permittivity of the material flowing in the pipe.

4 An embodiment of the invention includes a method and apparatus wherein the monitoring module and calculation module are adapted to provide the output data in a 6 form representing mass per unit volume of one or more materials or mixtures of 7 materials in the flow across plural cells of a cellular grid extending across at least a 8 portion of the cross-sectional area of the interior of the pipe.

Another embodiment of he invention includes a mcthod and apparatus wherein the 11 monitoring module and calculation module are adapted to provide the output data in a 12 form representing mass per unit volume of one or more materials or mixtures of 13 materials in the flow across plural cells ofa cellular grid extending across at least a 14 portion of the cross-sectional area of the interior of the pipe.

16 Another embodiment of the invention includes a method and apparatus ifirther 17 comprising a display device for visually displaying a sequence of images representing 18 the mass per unit volume of one or more materials or mixtures of materials in the 19 flow, and optionally comprising a storage device for storing the output data.

21 Another embodiment of the invention includes a method and apparatus wherein the 22 monitoring module comprises a transmitter system adapted to transmit 23 electromagnetic signals and a receiver system adapted to receive electromagnetic 24 signals, the transmitter and receiver systems comprising a plurality of electrodes located at angular positions around the circumference of the pipe; an analyser adapted 26 to determine the difference between the transmitted and received electromagnetic 27 signals; and a processor adapted to process the data representing the difference to 28 provide output data representing mass per unit volume of a mixture of the phases in 29 the multiphasc flow, the processing including at least one variable representing electrical permittivity of the mixture of the phases.

32 Another embodiment of the invention includes a method and apparatus comprising a 33 control system adapted to control the operation of the electrodes whereby the 34 electrodes are intermittently energised to act as a sequence of transmitter and receiver I pairs to provide a sequence of electromagnetic signals between the transmitters and 2 receivers across different regions of the cross-sectional area of the pipe.

4 Another embodiment of the invention includes a method and apparatus wherein the control system is adapted to control the operation of the electrodes whereby 6 successive electromagnetic signals have different electrodes acting as transmitters and 7 for each transmitter the remaining electrodes act as receivers.

S

9 Another embodiment of the invention includes a method and apparatus wherein the first control systcm is adapted to control the operation of the electrodes whereby in a 11 single monitoring cycle all of the electrodes sequentially act as a transmitter and for 12 each transmitter at least one or all of the remaining electrodes act as receivers.

14 Another embodiment of the invention includes a method and apparatus wherein the control system is adapted to control the operation of the electrodes whereby one or 16 more first electrodes are configured to act as transmitters and one or more second 17 electrodes are configured to act as receivers.

19 Another embodiment of the invention includes a method and apparatus wherein the transmitter and receiver systems comprise an annular array of electrodes around a 21 circumference of the pipe.

23 Another embodiment of the invention includes a method and apparatus wherein the 24 array of electrodes is arranged as a series of euived rectangles substantially covering the entire intemal surface of the pipe over a short axial length.

27 Another embodiment of the invention includes a method and apparatus wherein the 28 array of electrodes is arranged as a series of curved rectangles substantially covering 29 the entire external surface of the pipe over a short axial length where the wall of the pipe is electrically non-conducting and of any thickness.

32 Another embodiment of the invention includes a method and apparatus wherein the 33 electrically non-conducting pipe is mounted within an outer pipe made of any 34 material.

2 Another embodiment of the invention includes a method and apparatus wherein the 3 pipe and electrodes are adapted so as to be resistant to pressure and temperature.

Another embodiment of the invention includes a method and apparatus wherein the 6 variable representing electrical permittivity of the mixture of the phases of the 7 multiphase flow is converted to mass per unit volume using mathematical S relationships.

Another embodiment of thc invention includes a method and apparatus wherein the 11 parameters within the mathematical relationships used are derived from calibration by 12 comparing actual mass per unit volume within any portion of the pipe measured by 13 any independent method with the mass per unit volume within any portion of the pipe 14 calculated from the mathematical relationships used.

16 Another embodiment of the invention includes a method and apparatus wherein the 17 parameters within the mathematical relationships used are derived from calibration by 18 comparing an estimate of mass per unit volume within any portion of the pipe 19 measured by use of electrical measurements with the mass per unit volume within any portion of the pipe calculated from the mathematical relationships used.

22 Another embodiment of the invention includes a a method and apparatus wherein the 23 parameters within the mathematical relationships used are derived from calibration by 24 comparing estimates of mass per unit volume of one or more materials flowing in a pipe within any portion of the pipe measured by electrical process tomography with 26 the mass per unit volume within any portion of the pipe calculated parameters within 27 the mathematical relationships used.

28 Description of figures

Figure 1 shows electrodes distributed around a pipe cross-section containing flow 12.

31 10 indicates the pipe wall, and 11 indicates the electrodes which may be any number, 32 shape or arrangement around the pipe, inside, outside or within the pipe wall. Figure 33 Ia shows a cross-section of the pipe and Figure lb shows a longitudinal view.

2 Figure 2 shows the electrodes as curved rectangles. 10 indicates the pipe wall and 21 3 indicates the electrodes in the shape of curved rectangles which may be any number 4 around the pipe, inside, outside or within the pipe wall. Figure 2a shows a cross-section of the pipe and Figure 2b shows a longitudinal view.

7 Figure 3 shows examples of possible output data in the form of images or contour 8 plots. Figure 3a shows a transverse cross section of the pipe at the position 9 represented by the chain line 33, while Figure 3b shows a longitudinal cross section based at the position represented by the chain line 34. 30 indicates a contour at one 11 fixed value of in-situ density, 31 indicates a second contour at a second fixed value of 12 in-situ density and 32 represents a third contour at a third fixed value of in-situ 13 density.

Figure 4 shows a transverse cross-section of the pipe showing pipe wall 10, dotted 16 lines 30 indicating boundaries between zones 31. This example shows 13 zones (only 17 3 of which are labelled for clarity) but any number or arrangement is possible.

19 Figure 5 shows a graph of mixture peimittivity K plotted against volume fraction X for various models described in the text below.

22 Figure 6 shows a preferred embodiment of the present invention showing monitoring 23 module 61 mounted on pipe 10, calculation module 62, image display device 63, data 24 storage device 64 and connection to industrial acquisition and control system 69. the arrows 65, 66, 67 and 68 represent data flow.

27 Figure 7 shows a preferred embodiment of the present invention to calibrate the value 28 N used in equation 23 or 24 when the target industrial process involves dispersed 29 solids. A mass feeder 70 deposits solid materials 73 through a spreader 71 a twin-plane ECT system 72 and the monitoring module 61. The evenly dispersed solids 74 31 are flowing in the direction of arrow 75 within the pipe 10.

33 Figure 8 shows a preferred embodiment of the present invention to calibrate the value 34 N used in equation 23 or 24 when the target industrial porocess involves the flow of I one or more gases and liquids. A gas injector 80 injects gas bubbles 84 through a 2 mixing device 81 a twin-plane ECT system 72 and the monitoring module 61. The 3 evenly dispersed gas bubbles 84 are flowing in the direction of arrow 83 within the 4 pipe 10.

6 Figure 9 shows a graph of measurements of mixture permittivity against in situ 7 density for gravity-flow of semolina and fixed rods of semolina showing comparisons 8 with equation 23.

Figure 10 shows a grapgh of the same data as in figure 5 but at an expanded scale.

12 Example embodiments of the invention 14 In an embodiment of the present invention electrical measurements are used to measure the electrical permittivity of the materials flowing in the pipe or vessel and 16 those measurements are then processed to display and store images or grids of data 17 representing the in-situ density of the multiphase mixture present in the pipe. A 18 novelty of the present invention is that the in-situ density of the flow mixture is 19 derived directly from the measured permittivity without need to pass through the stage of calculating volume fraction. Figure 1 shows this example embodiment with flow 21 12 in a pipe 10 where a first set of electrodes 11 are placed in a regular or irregular 22 array. The electrodes may be inside, within or outside the body of the pipe. If the 23 electrodes are within or outside the pipe then the pipe wall at that point must be non- 24 conducting electrically. Figure la shows a transvese section of the example embodiment, while Figure lb shows a longitudinal view.

27 In a preferred embodiment of the present invention the first set of electrodes are 28 shaped as curved rectangles 21 covering substantially the whole of the outside area of 29 a short section of pipe as shown in Figure 2. Figure 2a shows a transvese section of the example embodiment, while Figure 2b shows a longitudinal view.

32 One or more electrodes are used as transmitters to generate an electric field across the 33 pipe and the permittivity of the material mixture is estimated from one or more I electrodes acting as receivers. A first data set representing a first image of the flow is 2 generated representing electrical pcrmittivity as measured by the first set of 3 electrodes. A second data set representing a second image of the flow is generated by 4 direct calculation representing in-situ density of the mixture using methods and equations described below.

7 Both the first data set representing a permittivity image of the product in the flow, and 8 the second data set representing in-situ density may be displayed as contour plots as 9 shown in Figure 3. In this example embodiment electrical measurements taken using clcctrodcs 11 mounted around thc pipc 10 arc convcrtcd into cstimatcs of in-situ using 11 the equations givenm below and displayed as conntours of different values 30, 31, 32.

12 The contour plot may be shown as a transvese section of the example embodiment, as 13 in Figure 3a, or as a longitudinal section shown in Figure 3b.

Other image types or data arrays may be shown in other embodiments for example the 16 data sets may divided in n zones or pixels, where n is ideally between S and 30 but 17 may be any number. Figure 4 shows an example where the flow cross-section within 18 the pipe 10 is divided into thirteen zones 41 by theoretical lines 40. Such zones or 19 pixels may be any shape or size to suit the application. When an embodiment using zones as shown in Figure 4 is used, the data sets may be shown as time series 21 representing conditions within individual zones.

23 Electrical imaging as proposed here is sometimes considered to be an ill-posed 24 problem and therefore incapable of producing accurate measurements of volume fraction. Cross in 2005 in reference [3] looked in detail at the bounds on 26 measurements typical of ECT (and other electrical measurement techniques) and 27 concluded: "..despite the ill-posed nature of the problem electrical imaging is a viable 28 technique for use in the volume fraction estimation of a two-phase mixture, and it is 29 quite feasible to expect to be able to recover accurate information." 31 Singha and Gorelick in reference [4] published in 2006 show that electrical resistivity 32 tomography (ERT) can be used to estimate groundwater solute concentrations if a 33 relation between concentration and inverted resistivity is used to interpret cross-well 34 tomograms. This relationship is similar in nature to those publsihed in references [1] I and [2] in that estimating concentration of a particular phase is a necessary part of the 2 procedure.

4 Electrical capacitance tomography can offer measurements unobtainable with other measurement technologies, but the interpretation of quantitative flow data requires a 6 good physical model of the interaction of the materials with the electric field in the 7 sensor and appropriate reconstruction and analysis algorithms.

9 In previous work on mass flow rate estimation from ECT, as described for example in reference [1] has been based on using the permittivity image to give a concentration 11 image, then multiplying by the velocity and concentration to give volume flowrate.

12 Volume flowrate of each phase is then multiplied by an estimated density of a 13 particular phase to derive a mass flowrate of that phase.

Measurements of electrical capacitance have been used to estimate the mass of tree 16 roots and other growth as described by Preston McBride Biyan and Candido in 2004 17 in reference [5]. The method used was to correlate the measured electrical 18 capacitance with root growth -this correlation is thus specific to the particular 19 geometry and material and is not capable of generalisation to other situations such as multiphase flow in pipes.

22 Below we give the background to the known mathematical models for this process 23 and then go on to re-write them in terms of in-situ density. Doing this enables us to 24 move directly from permittivity to density and thus to mass flowrate without needing the intermediate volumetric calibration.

27 The expression linking permittivitty to concentration of one material disperesd in 28 another in a multiphase flow is described by the company Process Tomography 29 Limited in reference [6] in an application note dating from 1999 and available on their website tomography.coin as the Maxwell equation: 32 K = K1. [2Ki + K2 -2.X.(K1 -K2)] / [2Ki + K2 + X.(K1 -K2)] (equation 1) I The expression applies to particles or bubbles of material permittivity Ki distributed 2 in a non-conducting medium of permittivity K2. The particles or bubbles occupy a 3 volume fraction X of the pipe section, where X may vaty between 0 (no dispersed 4 phase present) to approximately 0.6 particles packed closely together). Equation 1 is stated to be valid if the particles or bubbles of dispersed material are spherical and 6 uniformly distributed.

8 Van Beck writing in reference [7] in 1967 calls the expression shown in equation 1 9 the Rayleigh equation, states that is has validity up to a volume fraction occupied by thc sphcres up to approximately 0.2, and givcs the expression in the form: 12 Em=g 2 E1E2+2 (equation2) 1 2 E1E2V (e2-e1) 14 We will refer to equations 1 and 2, which are mathematically identical apart from notation, as the Maxwell-Rayleigh' equation.

17 Clarifying nomenclature: 19 K = c,n is the effective permittivity of a distribution of particles in another medium, K1 = c1 is the material permittivity of the continuous medium, 21 1(2 = E2 is the material permittivity of the distributed particles, bubbles or droplets, 22 X = v is the volumetric fraction of space occupied by the particles, bubbles or 23 droplets, 24 ". represents multiplication, i" represents division.

26 Wagner in1914 published in reference [8] a further original derivation of the electric 27 field through an array of distributed spheres. This solution was extended by Jeffrey in 28 reference [9], published in 1976 to give higher order terms. Taking only the dielectric 29 terms from Jeffrey's equation 1, equivalent to setting conductivity to zero or frequency to infinity, we obtain: 32 Em=ei(l ÷3 131c +3 fl?c2)÷°(c3) (equation 3) 2 where 82E1 E22 El 4 In this case the notation is as above except that c = X = v, the volume fraction. To avoid confusion we will not repcat Wagner's original equation here as the notation is 6 reversed from that of Jeffrey and van Beck, but Wagner's equations are equivalent to 7 the first two terms in equation 3 and will be referred to here as the Maxwell-Wagner 8 equation to I or 2" order.

For comparison purposes we will also refer to simple models where the flow is 11 represented by plates of material, either aligned in the plane of the electrodes so that 12 they are connected electrically in series, or normal to the electrodes where they act in 13 parallel. These simple systems are effectively the upper and lower bounds for all 14 permittivity-concentration models. See reference [6] for a more complete description of these expressions.

17 The parallel' model (equation 4) is the simple linear interpolation obtained if the 18 distributcd material were in uniform plates across the whole pipe at right anglcs to the 19 flow direction: 21 Kr = K1.(l-X) -I-K2.X (equation 4) 23 and the series' model (equation 5) would apply if the ditsributed material were in 24 uniform plates or rods along the axis of the flow: 26 K = [Ki. K2] / [K1.X + K2.(I -X)] (equations) 28 Van Beck in 1960 in reference [11] quotes from a publication by Sillars published in 29 1937 as reference [10] giving a more general form of Maxwell-Wagner: 31 ICE = K1[1 + N.X.(K2 -K1)/(K2 + (N-1).K1)] (equation 6) I where a new parameter N is introduced which is a function of particle shape. N=3 for 2 spheres in which case equation 6 reduces to the Maxwell-Wagner form (equation 3 to 3 first order in concentration). For oblate spheroids n 1 and for prolate spheroids N = 4 [b2/a2(n(2a/b)-1)f'. For a/b in the range of 1.5 to 2 which is perhaps typical of wheat grains, N would be in the range of S to 10. We will refer to equation 6 as the 6 Maxwell-Wagner-Si] lars (MWS) equation.

8 Hunt, Abdulkareem and Azzopardi published in reference [12] in 2010 an improved 9 and completely novel equation, introducing by analogy an equivalent factor N into cquation 1 to givc a more generalised form: 12 ICE = K1[1 + N.X.(K2 -Ki)/(K2 + (N-1).K1 -X.(K2 -K1)] (equation?) 14 This extended MWS (we will refer to it as eMWS) expression has the significant advantage that it allows for the particles to be non-spherical. N may take a value 16 anywhere between 1 and infinity but the equation reduces to other forms as follows: 18 N = 1: series model (equation 5), 19 N = 3: Maxwell-Rayleigh (equation 1), N ->co: parallel model (equation 4).

22 Van Beck in reference [71 also gives an expression (equation 8) derived by Looyenga 23 which is valid over the entire range of concentration from 0 to 1: K = lCi[1 + X.(K2"3 -K11'3)/K11'j3 (equation 8) 27 Changing all notation to be consistent and re-writing the equations in a similar form 28 we find: Parallel model: 31 KE = Ki[1 + X.(K2-K1)/K1] (equation 9) 34 Series model: 1 KB = Kill + X.(K2 -K1)/(K2 --K1))] (equation 10) 3 Maxwell-Wagner i order: 4 ICE = K1[1 + 3X.(K2-Ki)/(K2 + 2.I(i)] (equation 11) 6 Maxwell-Wagner 20(1 order: 7 KB = K1[1 + 3X.(Ka-Ki)/(K2 + 2.K1) + 3[X.(IQ-1(1)/(1(2 + 2.1(i)]2] 8 (equation 12) 9 Maxwell-Wagner-Sillars: K13 = K1[1 + N.X.(K2 -KO/(K2 + (N-1).KO] (equation 13) 12 Maxwell-Rayleigh': 13 KB = Kill + 3X.(K2-K1)/(K2 + 2.K1 -X.(K2-K1))] 14 (equation 14) Extended Maxwell-Wagner-Sillars: 16 1(13 = Kill + NX(K2 -Ki)/(K2 + (N-1).Ki -X.(K2 -Ki))] 17 (equation 15) 19 FigureS shows the curves for the various equations above over the full concentration range for a theoretical product disiributed as particles, bubbles or droplets with a 21 pcrmittivity of 1(2=6 in a continuous medium of permittivity K1 = 1. It should be 22 noted in looking at FigureS that equation 15 can bc made to be identical with 23 equations 9, 10 and 14 simply by choosing the value ofN to be x, 1 or 3. In addition 24 equationlScanalsobeusedwithanyothervalueofNintherangefromltoooto model particles, bubbles or droplets of any shape. It should be noted that the values 26 of perniittivity and parameter N are arbritrary to show as examples here and that any 27 physically realistic value may be used.

29 Existing ECT systems in usc arc calibrated by filling first with a material of permittivity K1 which is then defined as a concentration of X0, and then the sensor is 31 filled with a material of permittivity K2 which is defined as a concentration ofX=1.

32 This calibration procedure is veiy difficult when a sensor is mounted in an industrial 33 process, even if it is possible in a laboratory experiment. In order to overcome this 34 difficulty the present invention takes equation 15 further to be a function directly of I in-situ density. This is a novel derivation which enables ECT sensors to be calibrated 2 in the place of manufacture or elsewhere with products of varying dcnsity, so that 3 when installed in an industrial location there is no further need for calibration. This 4 proposed procedure which is a prefened embodiment of the present invention is thus a significant advantage to the operator of ECT equipment in an industrial plant.

7 The definition of volume fraction or concentration of the dispersed phase X is the 8 volume of a given space occupied by that material relative to the overall volume: X=V2/V (cquationl6) 12 where 14 V=Vi+V2 (equationl7) 16 V1 is the volume occupied by the continuous material of permittivity K1, V2 is the 17 volume occupied by the dispersed material of permittivity K2, and V is the total 18 volume of space under consideration. In the limit that we consider an short length of 19 pipe approaching zero the the volumes become identical to cross-sectional areas of pipe.

22 The mass M1 of the continuous matcrial is given by: 24 M1=D1.V1 (equation 18) 26 and the mass M2 of the dispersed material is: 28 M2=D2.V2 (equationl9) where M1 is the mass of the continuous material of permittivity K1 and material 31 density D1 nand M2 is the mass of the dispersed material of permittivity K2 and 32 material density D2.

I The in-situ product density' of each phase is defined here to be the total mass of the 2 respective phase divided by the total volume under consideration: 4 d1=M1/V (equation2O) 6 and 8 d2=M2/V (equation2l) Combining cquations 16,19 and 21: 12 X= d2/D2 (equation22) 14 and substituting equation 22 into equation 15 we obtain: 16 ICE =1(41 + N.d2.(K2 -Ki)I( 1)2.K2 + D2.(N-1).Ki -d2.(K2 -Ki))] (equation 23) 18 and inverting equation 23 enables us to calculate the unknown value d2 from 19 measurements as follows: 21 d2= [(KR-Ki).( K2 (N-l).Ki)] /[(K2-Ki).( 1(R (N-l).Ki)] (equation 24) 23 A preferred embodiment of the present invention is shown in Figure 6. A monitoring 24 module 61 is mounted on the pipe 10. 1(E is calculated by the calculation module 62 directly from capacitance measurements made in the monitoring module while K1, 1(2 26 and 1)2 are material preperties of the two products flowing in the multiphase flow. N 27 is dependent on the statistical average particle shape and in a preferred embodiment of 28 the present invention N is chosen by calibration as described below. The output data 29 from the calculation module is converted into a data set representing in-situ density which is then displayed as an image by a display device 63. Images may be displayed 31 in many ways as illiustrated by Figure 6, Figure 3 or any other normal means of 32 displaying data sets. The data may be stored on a storage device 64 and/or 33 transmitted to an industrial acquistion and control system 69.

I Using equation 24 measured permittivity may be converted directly to in-situ product 2 density without any recourse to volumetric calibration. This is of substantial 3 advantage to the users of capacitance-based flow measurement equipment relative to 4 the current procedures described above.

6 A similar analyisis may be carried out based on equationS or any other relationship 7 linking mixture perntittivity to concentration and all such models are explicitly 8 considered to be included in the present invention.

A preferred embodiment for the calibration of the factor N is to gcncrate a dispersed 11 flow in some suitable manner and to use ECT to calibrate the system. Specifically 12 the embodiment is to mount on the flow pipe two additional sets of electrodes 13 separated by a small axial distance. A third data set representing a third image of the 14 flow is generated at a relatively high frame rate using data fixm the second set of electrodes, the third image representing phase concentration at a second location 16 along the length of the pipe section. A fourth data set representing a fourth image of 17 the flow is generated at a relatively high frame rate, the fourth image representing 18 phase concentration at a third location spaced from the first and second locations 19 along the length of the pipe section. The third and fourth data sets are cross-correlated with respect to time to derive a fifth data set representing the speed of flow 21 along the pipe section between the first and second locations, also in the form of an 22 image or grid of data across the flow cross-section. The average of this fifth data set 23 is the mean velocity of the dispersed phase U2.

The mass flowrate m2 of the dispersed material is given by: 27 m2=D2.A2U2 (equation2s) 29 where A2 is the cross-sectional area of the pipe occupied by the dispersed phase.

Combining equation 24 with equation 21 32 d2= in2! (U2.A2) (equation 25) I This independently measured value of in-situ density d2can then be compared with 2 the calculation based on equation 24 and a value of N chosen so that the two results 3 match. This calculation may be done using the equation 26: N = [(1 -d2).(KE -K1). (K2 -K1)j/[Ki.((K2 -K1).d2 -(KB -Ki))j (equation 26) 7 A first preferred embodiment of the calibration method is shown in Figure 7 for 8 dispersed dry solids of permittivity K1 flowing under gravity in a gas of permittivity 9 1(2. A mass-feeder 70 is set to provide a fixed mass-flow rate m2 of dry solids 73 (for example wheat grains, but this may be any material to be used in the process to be 11 measured) into pipe 10, the material is dispersed across the flow using an appropriate 12 spreader 71 to obtain a uniform distribution of solids 74 moving in the flow direction 13 indicated by the arrow 75. The dispersed material velocity in the pipe Li2 is measured 14 by a twin-plane electrical capacitance tomography system 72 and the in-situ density of the dispersed product is calculated using equation 25. KB is measured using the 16 monitoring module 61. The value of N to be used in equation 23 or 24 is then 17 calculated from equation 26. The ECT system 72 and the monitoring module 61 are 18 to be mounted close together so that the velocity of the product is sensibly the same or 19 can be corrected by considering the acceleration due to gravity over the separation distance.

22 A second preferred embodiment of the calibration method is shown in Figure 8 for 23 dispersed gas of permittivity K1 flowing in a liquid, of permittivity 1(2. A suitable gas 24 injector 80 is set to provide a fixed mass-flow rate m2 of gas bubbles 84 into a flow of liquid 83. The gas is dispersed across the flow using a suitable mixing device 81 to 26 obtain a uniform distribution of gas bubbles 85 moving in the flow direction indicated 27 by the arrow 82. The dispersed material velocity in the pipe U2 is measured by twin- 28 plane electrical capacitance tomography system 72 and the in-situ density of the 29 dispersed product is calculated using equation 25. The value of N to be used in equation 23 or 24 is then calculated from equation 26. The ECT system 72 and the 31 monitoring module 61 are to be mounted close together so that the velocity of the gas 32 is sensibly the same or can be corrected by considering the acceleration due to gravity 33 over the separation distance.

I It should be understood that the embodiments described above are merely examples of 2 how to calculate the in-situ density of the dispersed phase and the value of N 3 associated with that phase, the same procedure may be used to calculate and calibrate 4 the values for the continuous phase.

6 In order to demonstrate the accuracy of equation 23, gravity-driven flows were 7 generated using a mass-flow feeder device. A commercial ECT twin-plane system S was then used to measure the velocity of the product and the mixture permittivity.

9 Example results arc given here using flour as the product. The arrangement of these itcms was similar to Figure 7.

12 Figures 9 and 10 show the same data on two different scales for gravity flows of 13 semolina in comparison with a fixed array of spaghetti, made of semolina. It can be 14 seen that equation 23 with a value of N=8 represents the semolina data with reasonable accuracy and that a value ofNl represents the spaghetti data well. Both 16 of these values of N are consistent with the known shape of the solids in these cases.

1 References 3 [1] Hunt A., Pendleton J. and Byars M. Non-intrusive measurement of volume and 4 mass using electrical capacitance tomography. ESDA 2004-58398, 7th Biennial ASME Conference on Engineering System Design and Analysis, Manchester, UK.

6 (2004) 8 [2] Hunt A., Pendleton J. and Ladam Y. Visualisation of two-phase gas-liquid pipe 9 flow using electrical capacitance tomography. ESDA 2004-58396, 7th Biennial ASME Conference on Engineering System Design and Analysis, Manchester UK.

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22 Agroforestry Systems 64, pp 305-309 2004.

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7 [12] Hunt A, Abdulkareem LA and Azzopardi BJ. (2010) Measurement of Dynamic 8 Properties of Vertical Gas-Liquid Flows. 7th International Conference on Multiphase 9 Flow ICMF 2010, Tampa, FL USA, May 30-June 4, 2010.