1992_Electrical Capacitance Tomography for Flow Imaging System Model for Development of Image Reconstruction Algorithms and Design of Primary Sensors

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Electr ical capacitance tomography for flowimaging: system model for development of imagereconstruction algorithms and design of primarysensorsC.G. XieS.M. HuangB.S. HoyleR.ThornC. LennD. SnowdenM.S. Beck

Indexing terms: Tomography, Image processing, Mathematical techniques

Abstract: A software tool that facilitates thedevelopment of image reconstruction algorithms,and the design of optimal capacitance sensors fora capacitance-based 12-electrode tomographicflow imaging system are described. The core ofthis software tool is the finite element (FE) modelof the sensor, which is implemented in OCCAM-2language and run on the Inmos T800 transputers.Using the system model, the in-depth study of thecapacitance sensing fields and the generation offlow model data are made possible, which assists,in a systematic approach, the design of animproved image-reconstruction algorithm. Thisalgorithm is implemented on a network of trans-puters to achieve a real-time performance. It isfound that the selection of the geometric param-eters of a 12-electrode sensor has significant effectson the sensitivity distributions of the capacitancefields and on the linearity of the capacitance data.As a consequence, the fidelity of the reconstructedimages are affected. Optimal sensor designs can,therefore, be provided, by accommodating theseeffects.

1 Int roduct ionThe 8-electrode capacitive tomography method for two-component flow imaging has been developed over thepast few years and has shown promising applications formulticomponent flow measurement [I-41. To expand theapplicability of this technique, improvements on thePaper 83 90 6 (E3, ElO), received 4th July 1991C.G. Xie, S .M. Huang and M .S. Beck are with the Department of Elec-trical Engineering and Electronics , UMIST, PO Box 88, Manchester,M60 lQD, U n i t ed Ki n gd omB.S. Hoyle i s with the Department of Electrical and Electronic Engin-eering, Univer si tyof Leeds, Leeds,LS2 9JT, n i t ed Ki n gd omR. Thorn i s with the School of Electronic Engineering, Unive rsi ty ofSouth Australia, Adelaide, South AustraliaC. Lenn i s with Schlumberger Cambridge Research Ltd . , PO Box 153,Cambridge, CB3 OHG, United KingdomD. Snowd en is with Schlumberger Industries Ltd . , Farnborough,Hamp s h ire , GU 1 4 7PW, U n i t ed Ki n gd omIEE PROCEEDINGS-G, Vol. 139, N o . I , F E B R U A R Y 1992

spatial resolution of the system must be made. To achievethis objective, first, the number of electrodes around theperiphery of a pipe should be increased. The number ofextra electrodes that can be added is governed by thecapability of the transducer hardware in resolving verysmall capacitances. The improved design of the capa-citance transducer electronics has enabled the use of a12-electrode capacitive sensor [SI; this will more thandouble the independent capacitance measurements (from28 to 66, see eqn. l), which means that twice the numberof objects in the field of view can be resolved.The second aspect of enhancing the image resolution,which forms the focal point of this paper, is to improvethe image reconstruction algorithm, which is, as willbecome clear later, strongly related to the design of aprimary capacitance sensor. A poorly designed capa-citance sensor can produce extremely nonlinear measure-ment data, leading to erroneous reconstructed images.The reconstruction algorithm should also be efficient sothat a real-time performance (say 20 frames per second)can be realised on a network of transputers.The aim of the work presented in this paper is todevelop a software environment, as shown in Fig. 1,facilitating the design of an image reconstruction algo-rithm and the optimisation of a 12-electrode primarysensor for a six inch gas/oil pipeline. The core of this soft-ware environment is the finite element (FE) model of thesensor system; it is capable of calculating the field sensi-tivity information needed by the image reconstructionprocess, and also produces simulated capacitance meas-urement data for predicting the performance of a com-plete capacitance tomographic system.2 Fini te element model : the for ward problem2.1 Mathematical formulation of the sensor modelIn this study, a two-dimensional (2D) FE model of thesensor system is described. This confines us to deal withan object which is translationally uniform. The calculatedcapacitance is in units of F m-'. The model is describedfor gas/oil two-component flow, however, other two-component flows can be treated similarly.A 12-electrode capacitance sensor is shown in Fig. 2.To establish its mathematical model, it is necessary to

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electrode system has about 2000 nodes; to store matrix A(as single precision 32-bit data), it demands about 16Mbytes of memory. Since matrix A is very sparse (i.e. ithas many zero entries) and is often banded, it can bestored in two vectors (a real and an integer) in a com-pacted fashion containing fewer entries using the 'skyline'scheme [6, 71. In doing so, the storage needed, for a2000-node system, is usually less than 1 Mbyte, which iswell within the memory limit of today's powerful micro-computers.

After solving node potentials from eqns. 4 and 5 , thecapacitance of the electrode pair i - , can be calculatedby performing the following line-integration numerically:Ci, = Q rj)/K

= E O / V J E(x, Y ) V P ( X ,Y) zj ( 6 )( X , Y ) S T ,where Q(rj)s the charge sensed by detecting electrode jj= i + 1, . , 12), and $I(')(, y), represented by di) in adiscrete form, is the potential distribution when electrodei is the source electrode and when a flow E (x , y ) , rep-resented by vector E (and therefore E * ) in a discrete form,is present.The F E model of the 12-electrode system is imple-mented in OCCAM-2 language running on Inmos T800transputers [SI. This makes it easy to integrate thesystem model with the image reconstruction process foralgorithm development and testing (Section 3). Theproved image reconstruction algorithm can then beimplemented on several transputers to realise real-timeperformance (Section 6). In this research, an InmosB004-compatible PC add-in board, on which there is aT800 20MHz transputer with 4 Mbyte dynamic RAM, isused to perform the FE calculations, as well as serving asthe transputer development system (TDS) [SI. For a2000-node system model, the transputer completes the 66capacitance calculations (C, j , i = 1, 2, . , 11, j = i + 1,..., 12) within 90 seconds, which is considered fastenough for our modelling purposes. Obviously, this cal-culation time can be reduced by distributing the FE cal-culation processes over several transputers running inparallel.2.2 FE model I : calculation of capacitance field

sensitivityTwo F E models (processes PI and P2) have been estab-lished see Fig. 1). Process PI calculates the field sensi-tivity (02) needed by the image reconstruction process(P3), for a primary sensor having the geometrical andphysical data D1. With reference to Fig. 2, data D1include R,, R,, R, , 6 , d, E,,, ep , , and coil, where d isthe length of the projected guard, E,, and epl are, respec-tively, the dielectric constants of the screen-electrodeinsulator and the pipe-liner.The field sensitivity distribution of electrode pair i - ,Si,k), is defined as

where( 7 4

A&= coil- ( 7 4and where Ci, k) is the capacitance when the kth in-pipeelement (the element inside the circle with radius R,) hasdielectric constan t and the rest of the in-pipe elementsall have that of egos (in our model, there are 900 n-pipeIEE PROCEEDINGS-G, Vol. 139, N o . I , F E B R U A R Y 1992

elements, i.e. the vector E* has 900 entries; k = 1, 2, ...,900). Ci . ( g a s ) and Ci, (o i , ) are, respectively, the capa-citances when the pipe is filled with gas and with oil;ACi. , is, therefore, the fullscale capacitance change. Notethat in this paper Cf, ( g o s ) are called the system standingcapacitances. p ( k ) s a correction factor related to the areaof the kth in-pipe element; p ( k ) has different values forelements of different areas.In process PI, owing to. the property of symmetry,only 6 out of 66 distributions of field sensitivity need cal-culating; they are S , . (sensitivity distr ibution of anadjacent electrode-pair, type I), Sl,, that of an electrode-pair separated by one electrode, type 2), Sl,. (that of anelectrode-pair separated by two electrodes, type 3), Sl,(that of an electrode-pair separated by three electrodes,type 4), S l . (that of an electrode-pair separated by fourelectrodes, type 5 ) and SI , , (that of a diagonally separ-ated electrode-pair, type 6). This can significantly reducecomputation time since the rest of the 60 sensitivity dis-tributions can be obtained by simple rotation transform-ation (discussed below). To make these six sensitivitydistr ibut ions accessible by the image reconstructionprocess P3, a procedure is used in PI to transform themfrom the FE domain (which has 900 n-pipe elements ofdifferent areas distributed irregularly) to the imagedomain (which has 812 in-pipe square picture-elementsor pixels having the same area), i.e.

( 7 4where Q , @) are the transformed sensitivity distributionsin the image domain and p the pixel number @ = 1, 2,. 812); T{ } denotes the transformation operator. Thelinear transformations involved are scaling (the sensorgeometry has different units in two domains), translationand ref lection (if different co-ordinate systems are used in

Qi&) = T{S, . , ( k) } i = 1 and j = 2, 3, ..., 7)

0 d

b e

C fFig.3 Capacitance sensitivity distributions of six typicol electrodepoirs calculated for sensor 2R,=76,2mm,R,-R,=15mm,R,-R,=7mm,d=9mm,O=26 ,&,=4,E = 5.8, cw = I and so,, = 3.:'adjacent electrode p a i r , K l l , Ib electrode p a i r separated by one electrode,nL,,c electrode pair separated by two eleclrodes, Cl,,.d electrode pair separated by three electrodes, n,,e electrode pair separated by low electrodes. n .f diagonally separated electrode pair,n,,

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two domains), and interpolation or extrapolation ofsensitivity values for each pixel p.

Fig. 3 shows the typical six transformed sensitivity dis-tributions Q,,, to a (type 1 to type 6), for a sensor(sensor 2 in Section 4.2) with R , = 76.2 mm, R , - R, =15 mm, R , - R , = 7 mm, d = 9 mm, 0 = 26 ,E,, = 4 and= 5.8. It shows that the field sensitivity is higher nearthe pipe wall than in the middle of the pipe, and in someareas the sensitivity exhibits positive response, otherwiseit is negative (the sunken areas) or zero. The area of posi-

tive response interrogates different parts of the pipecross-section for different electrode pairs.To obtain the other 60 sensitivity distributions, inprocess P1, rotation transformations are furtheremployed in the image domain (the centre of the pipe isthe centre of rotation), i.e.

Qm, = R{Qi, ; Y (74where R{ . } is an operator representing rotation trans-formation. Eqn. 7e is interpreted as tha t a,,,, " is obtainedby rotating ai,nticlockwise by y degree. Note that Qm,and Qi, must be of the same type.Table 1gives a full listof the relationship associated with eqn. 7e.2.3 FE model 11: simulat ion of capacitancemeasurements due to various gasloi l flowdist r ibut ionsVarious gas/oil distribution models 03, represented byE(x, y ) or e (and therefore e*) in eqn. 6, are generated by adifferent F E model (process P2, see Fig. 1). The corres-ponding responses of a sensor (with geometrical data Dl),namely, the 66 capacitance data (04), are then calculatedby process P2, serving as the flow 'measurement' d ata forthe image reconstruction process P3 (Section 3). Inprocess P2, realistic flow models of different 'regimes',such as stratified flow, core flow, annular flow, gas-bubble flow and oil-droplet flow, can be produced byassigning the corresponding entries of the vector e* witheither E#- or Flows of different volume fractions ofoil 0 arious orientations of gas/oil interfaces in thecase of stratified flows, different numbers and sizes ofbubbles or droplets can be generated.Fig. 4a shows an example of a stratified gas/oil flow(data 0 3 in Fig. I), where the oil phase is represented bythe high grey level B=0.603) and the gas phase by thelow one. Fig. 4b shows the corresponding 66 normalisedcapacitances Ai (data 04), calculated for the primarysensor 2 (Section 4.2). The normalised capacitance Ai isdefined as

Ai. = (C; j Ci. g.wJ/ACi j (8)where C ; j is the capacitance measurement due to agas/oil distribution model. For a linear system, 0 1 (called 'over-shooting'). The magnitude of overshooting is, in general,

larger than that of the undershooting. This nonlinearityin the capacitance data is caused by the effects of theguard electrodes and the discontinuity in the distribution

Fig. 4(I a stratilied &oil flow model, where the high grey level represents the oil phaseand the low the gasb the corresponding 66 normalised capacitancesAs f flow model (a) calculatedfor sensor 2c image reconstructed using L,,, and the improved backprojection algorithmusing full sensitivity data as shown in Fig. 3d image recons tructed using the TJ/l alg orithm'

Typical display on the transputer graphics monitor

of dielectric constants e*. With respect to the situationswhen there is only gas or oil in the pipe, the presence of agas/oil mixture will redistribute the electric flux lines inthe system. This redistribution may cause some detectingelectrodes to absorb more (or less) electric flux lines thanwhen the pipe is filled with oil (or gas), resulting in over-shooting(or undershooting) effects.3 Image reconstruct ion: he inverse problemFor a capacitance tomography system, the inverseproblem is to determine the distribution of dielectric con-stants of gas/oil components (the vector e*) from themeasured 66 capacitances Cis , i.e. to find the inverse ofeqn. 6. It should be pointed out that there is no exact/analytical solution to such an inverse problem.Important features associated with the capacitancesensing field are that, the electric flux lines, expressed byfield vector E(x , y)V&x, y ) . tend to spread, and worst ofall, are related to the object ~ ( x , ) to be imaged (also seeeqns. 2 and 6). This is distinctly different from othertomography techniques, such as the X-ray CT, where thesource lines pass directly through the object to beimaged. Therefore, we call the capacitance field a 'softfield', which is inherently nonlinear, and the related prob-lems the soft field problems. Because of these features, theimage resolution of a capacitance tomography system ispoor in comparison with the X-ray CT (the electric fluxlines are difficult to focus), and the well developed imagereconstruction algorithms for X-ray CT cannot directlybe used for capacitance tomography. However, since acapacitance tomography system has very fast response, is

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Table 1: List of other 80 sensitivity distributions Cl.,.. versus the typical 6 onesa,.,nd the corresponding rotation angle 7' I n m ,'1.2 ' ' 4.5 5 . 6 , 7 7.8 '6 .9 9.10 'l0.11 ' ?1 ,12 ' 1.12? , a '2.4 ' 4,s '5.7 '6.8 n7.9 '8 .10 '9 .71 1 0 . 1 1 ' , , ? I ' 2.12

'1.4 '2.5 ' '4 .7 '5.9 '6.9 n 7 , 1 0 ' , I 1 '9 .72 '1.10 '2.13 '3.121.5 2 . B ' 4.8 '5.9 '6 .10 n 7 . r l '6 .12 '7.9 '2.10 '3.11 ' 6 1 2n1.6 2 . 7 ' '4 .9 '5 .10 S.11 ' 7.12 '1 .8 2.9 '3.30 '5 .12'1.7 '2.8 '3.9 '4 .70 '5.1? '6.12y 30" 60 90 120" 150" 180" 210" 240" 270 300 330

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. -adaptive threshold operation is required. Numericalexperiments have suggested that the following thresholdoperation is suitable (in our imaging system, 256 integergrey-levels, 0-255, are used).

0 if C@) < qcl@) { 55%) otherwise

where the threshold level q is (0< q < l),q = 1 - 0.5a)C (lob)

and where

AVG( ) {forGtp > 0)) (104where A V G ( . ) denotes an average operator and {. . .} aconditional statement.

To illustrate the effectiveness of this algorithm, Fig. 4cshows the reconstructed image (data 0 5 , see Fig. 1) usingthe capacitance data 04 hown in Fig. 46, which closelyresembles the flow model 0 3 (Fig. 4a).The image recon-structed using the 0/1 algorithm' and a similar thresholdoperation is shown in Fig. 4d; t has poorer fidelity incomparison with Fig. 4c (process P4 n Fig. 1is involved).

To illustrate the capability of the capacitance tom-ography system in distinguishing multiple objects, agas/oil flow model depicted in Fig. 5a is used, where thetotal oil concentration B = 0.203. The correspondingcapacitance data from sensor 2 (Section 4.2) areshown in Fig. 5b. From the reconstructed image (Fig. 5c),the presence of four individual 'oil droplets' can hardly beidentified, especially the two nearer the centre of the pipe.This indicates the inherent limitation with a capacitancetomography system; it has a position-dependent spatialresolution over the pipe cross-section. When a smallobject moves from near the pipe wall towards the pipecentre, the images reconstructed change from being sharpto being seriously blurred.

For comparison, the image reconstructed using the'0/1 algorithm' is also displayed (Fig. 5 4 , indicating aneven poorer distinguishability.4

4.1 Sensor design parametersThe structure of a primary sensor will no doubt influencethe performance of a capacitance measurement system.FEM has been used to study the effects of variations ofsensor parameters on the capacitance sensitivity dist ribu-tions and on the system response [lo]. The designparameters associated with a 12-electrode sensor are (seeFig. 2)

Image f idel ity against sensor structure: t hesensor design

(a) , the pipe radius.This parameter is fixed for a particular pipe line. For asix inch (I.D.) pipe, R , = 76.2mm. Other parameters R,- R , and R , R, discussed below are based on a sixinch pipe.(b) R, R , , E ~ ~ :he thickness of pipe-liner with dielec-tric constant E ~ ~ .Ideally, should be small to minimise the field diver-gence. However, other factors, such as the requirementsof corrosion, abrasion and temperature resistance, andthe temperature stability, may limit the selection of thepipe-linear material. The machinable glass (ceramic) usedfor our sensor hasSmall R, - R , would be desirable to save materialand, therefore, to reduce the cost of the sensor. However,94

= 5.8.

it should be borne in mind that the requirements ofmechanical strength of the sensor to withstand certainpressures and the ease of machining mean that there is aminimum thickness for the pipe-liner (not smaller than10mm in our case). More importantly, R, - R , has asignificant effect on the performance of the imagingsystem and should be carefully selected. This will be illus-trated in Section 4.2.

c) R? - R 2, ~ ? : he thickness of screen-electrode insu-lator with dielectric constant E,, .An earthed screen is necessary to eliminate the exter-nal electrical interferences and t o protect electrodes fromdamage. Small R , - R, would make the sensor compact,but theoretical and experimental studies have found thatdecreasing R 3 - R, will reduce the standing capacitancesof the sensor system [ S , IO]. It is possible that these

capacitances may become too small to measure. There-fore, when selecting this parameter, the measurementresolution of the capacitance transducer hardware mustbe taken into account. It has been found that R, - R , =7 mm is suitable for our sensor and transducer systems.The selection of E, is not crucial. Potting material isused as the screen-electrode insulator for our sensor, andit has E,, = 4.(d)0: the size of electrode.For a 12-electrode system, 0 must be smaller than 30 .A larger 0 will give rise to larger standing capacitances ofthe sensor (especially those of diagonally separated elec-

trode pairs, their increases would be most beneficial forthe capacitance measurement circuit) and higher capac-itance sensitivities, and is therefore desirable. To allowsome space for the projected guards (see below), 0 = 26has been selected for our sensor. The axial length of eachelectrode is 10cm.

(e) d: the length of projected guards.The introduction of projected guards has been foundto be an effective means of reducing the standing capac-

itances of the adjacent electrode-pairs significantly. Notethat this will also reduce the standing capacitances ofother electrode pairs but to a much lower percentage(Fig. 7). The transducer hardware will benefit most from3 I ,012

1 - 2 1 - 3 1-4 1-5 1-6 1 -7electrode pair

Fig. 7 Calculated standing capacitances of six typical electrode pairsfor sensors with projected guards (d = 9 nun, sensor 2) and without pro-jected guards (d = 0, sensor 2 A )Note that differentvertical scale is used for electrode p-3r 1-2Other sensors' parameters are R , = 16.2 nun. R, - R , = I5 mm, R, - R , =7 mm. 0 = 26 . E= = 4, E,, = 5.8, EThe axial length of each electrode^ 10cm0 Sensor 2Sensor2A

= I and so,, = 3

this design since a very large standing capacitance wouldmake balancing the capacitance-measuring circuit diffi-cult (in the present circuit design, the maximum standingcapacitance allowed is 2 pF [SI). A value of d = 9 mmIEE PROCEEDINGS-G, Vol. 139, N o . I F E B R U A R Y 1992


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has been found suitable. It has been observed that the useof projected guards has a minor effect on the fidelity ofthe reconstructed images.The electrodes and the projected guards are assumedto be very thin in this FE model. This is justified since in

example, Figs. 9.la, 9.2a and 9.3a show the same strati-fied gas/oil flow model (B= 0.20) used for this purpose.Fig. 9.lb, 9.2b and 9.36 give the corresponding 66 nor-malised capacitances A i , obtained by sensors 1, 2 and 3,

struction, three sensors with different thicknesses of pipe-liner are investigated; they are sensor 1 with R, R I =10mm, sensor 2 with R , R I = 15 mm and sensor 3with R, R I = 20 mm; other sensor parameters arefixed and they are R I = 76.2 mm, R , - R, = 7 mm,d = 9 mm, 0 = 26 , E,, = 4 and E ~ , 5.8 (Section 4.1).Sensitivity distributions Q , of the three sensors werefirst calculated (Section 2.2). Fig. 6 shows the plots ofweighting factors W@),calculated from ai, (eqn. 9b).Plot W @ ) an give an indication of the uniformity of thecapacitance sensitivity distribution. More uniform W(p)means that there is a smaller difference between the sensi-tivities near the pipe wall and in the middle of the pipe,and therefore less correction is needed for the imagereconstructed (eqn. 94. In this sense, sensor 2 with R,R I = 15 mm is a preferred choice. Field uniformitycan also be seen from the sensor's fullscale capacitancechange, ACi, , shown in Fig. 8. It can be seen that,

b

1 - 2 1 - 3 1-4 1 - 5 1 - 6 1 - 7electrode pair

Fig. 8 Calculated full-scale capacitance change of s ix typical electrodepairs for sensor I ( R , - R , = IO mm , ensor 2 R, - R , = I5mm ndsensor 3 ( R , - R , = 20 mm)Other sensors' parameters are: R , = 76 2 mm, R , ~ R , = 7 mm, d = 9 mm,8 = 26 . E, = 4, E ~ , 5.8, E- = 1 and E. = 3The axial length of each electrode s IO mSensor 3Sensor2Sensor I

ACl. ,/AC1,, is 5.2 for sensor 2, whereas for sensor 1 thisratio 1s 11.9, which is more than doubled. For sensor 3,ACl,,/ACl, is 1.4, which is abnormally small and isfound to be the cause of severe nonlinearity present in thecapacitance data (see below).Simple flow models can be used to visualise the fidel-ities of the images reconstructed using these sensors. For

Fig. 9(a)s) sing three different sensors(I sensor 1 with R, - R , = IO mmb sensor 2 with R, - R, = 15 mmc sensor 3 with R, - R , = 20mmThe rest of the sensors' parameters are R , = 76.2 mm, R, - R, = 7 mm,d = 9 mm, 0 = 26 , = = 4, E#, = 5.8, E- = I and E - , ~= 3All Egure b)sdepict the sensors' capacitance data i. ,All figure (cb show the images reconstructed using the improved backprojection

Image reconstruction of a stratifiedflow (that shown in all Fig.

algorithmAll figure (d)sshow those using the '011 algorithm'

respectively. It can be seen that the capacitance data fromsensor 3 exhibit severe nonlinearity (large-scale over-shooting and undershooting, see also Fig. 10.3b). This iscaused by the selection of the pipe-liner (20 mm); it is sothick that the sensing fields of adjacent electrode pairsare concentrated mostly in the pipe-liner. This is whyACl, /AC1. is abnormally small for sensor 3 (see Fig. 8).Images reconstructed from the appropriate capa-citance data, using the improved backprojection algo-rithm (Section 3), are shown in Fig. 9.lc, 9 . 2 ~nd 9. 3~ . ycomparison, the image reconstructed from sensor 3 hasthe poorest fidelity because of the severe nonlinearity ofthe capacitance data mentioned above, and that from

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sensor 2 has better fidelity than that from sensor 1. Forthese three sensors, images reconstructed using the 0/1algorithm are also shown in Figs. 9.ld, 9.2d and 9.3d,respectively. These images all have poorer fidelity than

Fig. 10in al lfigure (a b) using three diffment sensorsa sensor I with R, - R , = IOmmb sensor 2 with R, - R, IS mmc sensor 3 with R, - R , = 20mmThe rest of the sensors parameters are K , = 16.2 mm, R, - R, = 1mm,d = 9mm, 0 = 26. 6- = 4, E = 5.8, E~ = 1 and E ~ , ,= 3All figure (b)sdepict the sensors capacitance data A ,All figure cb how the images reconstructed using the improved backprojectionalgorithmAll figure(@ show those using the Oil algorithmtheir counterparts obtained from using the improvedalgorithm, and they exhibit no significant difference fromeach other since the sensitivity data of each sensor, afterthe 0/1 binary operation, have virtually no difference.Many other flow models have been used to test theperformance of these sensors, and it has been found thatsensor 2, in virtually all the cases, delivers the best imagefidelity. To reinforce this finding, another gas/oil flowmodel B= 0.291) and the corresponding reconstructedimages are given in Fig. 10.

In summary, from the point of view of high fidelity ofreconstructed images, which is the ultimate criterion ofany tomography system, sensor 2 with R, R I = 15 mmis an optimal design. Note that, for other two-component

Image reconstruction of two oil droplets in gas (that shown

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flows, such as an oil/water flow, this optimal sensor is notnecessarily the optimal one. A similar approach can beused to redesign the sensor.

1 0

0 8No 060 46

0 2

00 -00 0 2 0 4 0 6 0 8 1 0beta

beta b

0 0 2 4 06 0 8 10beta CFig. 11 Oil concentrations calculated jiom the image B,) andfrom theaverage of the 66 normalised capacitances @J against the concentrationof theflow models0D stratified lowb annular flowc coreflowThe straig ht Line(w ith no symbols) shows the ideal relationship-m- beta2-A- beta1

5 Concen tration measurement of f low

The simplest way to determine the oil concentration of agas/oil flow is to sum up all the pixels that have greylevels above the threshold (eqn. loa); this sum is thendivided by the total number of pixels in the pipe (812 forour imaging system). The resulting oil concentration isdenoted as /I1.The accuracy of this method dependslargely on the precise use of the threshold level, whichhas been found to be difficult to achieve. The results ofp,against oil concentration of gas/oil flow model /I are

components

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shown in Fig. 11for stratified flows, annular flows andcore flows. Fig. l l a indicates that the method of deter-mining oil concentration from the image works quite wellfor stratified flows. However, the results for core flows arethe most erroneous (Fig. llc); because of the inherentlylow spatial resolution in the centre of the pipe, the imagesfor core flows are blurred and occupy a larger pixel areathan the real flows do; consequently, oil concentrationsare overestimated, especially at low oil concentrations0 .For annular flows (Fig. llb ), the discrepancy betweenand B is also unacceptably high, in particular at high oil-concentrations.An alternative, and simpler, method has been used toreduce the measurement error; it uses the average of the66 normalised capacitance measurements as an indica-tion of oil concentration, denoted asB 2 ,The results of B2 against are also shown in Fig. 11forthe above three flows. Again, for stratified flows, p2 and phave maintained the closest agreement (Fig. lla); forannular flows, the use of p 2 , instead of P I has substan-tially reduced the measurement error (Fig. llb). Theaccuracy for core flows is also improved to a large extent(Fig. 1C), hough the oil concentration is underestimatedbut the monotonic relationship between p 2 and p isobtained, making the correction much less difficult.To increase the accuracy of concentration measure-ment further, calibrations of the sensor system for variousflow regimes are needed. An expert system approach is tobe developed to recognise the various flow regimes fromthe distribution of the capacitance data, and the corres-ponding calibration data for the identified flows can thenbe retrieved.6 Parallel implementation of image

The image reconstruction algorithm described in Section3 is implemented using a transputer-based system. Ittakes about 100 ms for one T800 (25 MHz) transputer tocomplete one image reconstruction; this is equivalent to

8 2 = A V G ( l l i . j l ) (11)

reconstruct ion algori thm

host 8 monitor (TB) master & graphics (T8)throughputfrom master I

backprojector

throughputw r kIII

to result II

ackproectorrom hostto host ork done* feedback feedback__..

to PC I I from PC to controller I ltrom controller I Drocessorl processor n

an imaging rate of about 15 frames per second. It hasbeen found that nearly three-quarte rs of this time is spentwaiting for values to be fetched from and written tomemory, accounting for a great percentage of an applica-tions total running time. The investigation of ways ofdecreasing memory bottleneck time becomes adeveloping issue [12].For our flow imaging system, to increase the imagingspeed, multiple transputer-based processors can be usedin parallel to implement the backprojection algorithm.One of the simplest, and often the most efficient, ways ofexploiting parallel processing is to distribute independenttasks to each of the processors. Such a configuration ofthe system is often called a task farm [13]. Thetransputer-based capacitance tomography system isorganised in this way as a load-balancing pipeline (Fig.12). The task farm consists of a master processor (T80025 MHz with 1 Mbyte VRAM), whose function is to dis-tribute the tasks (a stream of the 66 capcitancemeasurements) and collect the results (the correspondingreconstructed images and flow concentrations), and somenumber of slave processors (T801 25 MHz typically with2 Mbyte DRAM), that actually do the work (each slaveprocessor executes the same serial program he back-projection algorithm n its own data set). In a load-balancing pipeline, several buffer processes (thethroughput and the feedback) carrying tasks toworkers, and results to the display are also run on eachslave processor, ensuring that whenever a slave processorcompletes one task another is immediately available.Other processors in the task farm are: (i) a processor(host and monitor) handling the external I/O; this is aPC-hosted transputer (T800 20 MHz with 4 MbyteDRAM on a PC add-in card; Inmos BO04 compatibleand used as TDS), performing the booting of other pro-cessors in the network, monitoring (via VDU), keyboardinput and loading/saving data from/to the PC hard-disk;(ii) a processor (T222 or T414 20 MHz with, say, 8 KSRAM) controlling the remote sensor electronic circuitry[ 5 ] which acquires capacitance data needed by themaster processor for distributing over the task farm. The

I_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - _ _ _ _ ----I main node slave (T8) end node slave(T8) II . I I I

task farm

to wmr j frOm semoiFig. 12tion algorithmIEE PROCEEDINGS-G, Vol. 139, No. I , F E B R U A R Y 1992

Transputer-based multi-processor syste m with task farm configuration used fo r implemen ting in parallel the backprojection ima ge reconstruc-

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master processor also executes the process which displaysgrey-level images of flows on a graphics monitor .The speed-up of imaging frame rate when differentnumbers of slave processors are used is shown in Table 2.Table 2: S peed-up o f im ag ing f r am e r a teNo. f slave-processor image framelsec speed -up1 10.5 1 o2 20.3 1.933 29.4 2.80

The speed-up is almost linear. It can be predicted that,to achieve 50 frame/second imaging speed, at least 5T800 slave processors should be used (if the graphicstransputer is fast enough).7 ConclusionsThis paper has demonst rated the capability of a softwaretool facilitating algorithm development and sensor designfor capacitive tomography systems.

The backprojection algorithm has been improved,producing images with better fidelity. The primary sensorhas been optimised for a gas/oil two-component flow,minimising nonlinearity in capacitance measurements. Amethod for determining volume concentration usingcapacitance measurements has been proposed.Imaging speed can be significantly increased by usingInmoss new generation transputers, code-named H 1. TheH1 transputer retains compatibility with the T800 series,and is ten times faster in both processing and communi-cation speeds. It c an be anticipated that, using H1 trans-puters, a 100 frame-per-second imaging speed can bereadily achieved. The software tool described in thispaper will also benefit from the introduction of the H1transputers, running ten times faster.

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8 A c k n o w l e d g m e n tThe authors acknowledge the Science and EngineeringResearch Council and the Department of Trade andIndustry for supporting this work through a grant underthe LINK scheme.

9 R e f e r e n c e s1 HUANG, S.M., PLASKOWSKI, A., XIE, C.G., and BECK, M.S.:Tomographic imaging of two-component flow using capacitancesensors,J . Pkys . E, 1989,22, (3) , pp. 173-1772 XIE, C.G., PLASKOWSKI, A., and BECK, M.S.: electrodecapacitance system for two-component flow identification. Part 1:Tomographic flow imaging; Part 2: Flow regime identification,IEEh o c . A , 1989,136, (4). pp. 173-1913 SALKELD, J.A.: 1991 PhD thesis, University of Manchester4 THOR N, R., HUANG, S.M., XIE, C.G., SALKELD, J.A., HUNT,A., and BECK, M.S.: Flow imaging for multi-component flow mea-surement, Flow Meas. nst rum. , 1990, l, (4), pp. 259-2685 HUANG, S.M., XIE, C.G., THOR N, R., SN OWDEN, D., andBECK, M.S. Design of sensor electronics for electrical capacitancetomography, IEE Proc. G, 1992 , 139 , ( l ) , pp. 83-886 SILVESTER, P.P., and FERRARI, R.L.: Finite element for electri-cal engineers (New York: Cambridge University Press, 1990) 2ndEdition7 HUGHES, T.J.R.: Th e finite element method inear static anddynamic finite element analysis (Prentice-Hall International, 1987)8 Transputer reference manual. Inmos Ltd (New York: PrenticeHall, 1988)9 TransD uter develoDment svstem. Inmos Ltd N ew York: PrenticeHall, i990) 2nd Edition .IO XIE, C.G., S T O m , A.L., PLASKOWSKI, A., and BECK, M.S.:Design of capacitance electrodes for concentration measurement oftwo-phase flow, M e a . Sci. Tecknol., 1990,1, (1) .pp. 65-78KHAN, S., and ABDULLAH, F.: Computer-aided design ofprocess tomography capacitance e lectrode system for flow imaging.Proc. 5th Conf. Sensors and their applications, September 1991,Edinburgh, pp. 209-214LOSHIN, D.: Making every bit count, Parallelogram, 1 9 9 1 , pp.12-14BOWLER, K.C., KENWAY, R.D., PAWLEY, G.S., ROWETH, D.,and WILSON, G.V.: An introduction to OCCAM 2 programming(Studentlitteratur: Chartwell-Bratt, 1989) 2nd edition

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1992_Electrical Capacitance Tomography for Flow Imaging System Model for Development of Image Reconstruction Algorithms and Design of Primary Sensors