Various aspects and results of 2-D finite element (FE) modeling of electrostatic fields in 12-electrode capacitive systems for two-phase flow imaging are described. The capacitive technique relies on changes in capacitances between electrodes (mounted on the outer surface of the flow pipe) due to the change in permittivities of flow components. The measured capacitances between various electrode pairs and the field computation data are used to reconstruct the cross sectional image of the flow components. FE modeling of the electric field is necessary to optimize design variables and evaluate the system response to various flow regimes, likely to be encountered in practice. Results are presented in terms of normalized capacitances for various flow regimes. The effects of key geometric parameters of the electrode system are presented and analyzed

Abdullah, F.

Khan, S.

English

City Research Online

              City, University of London Institutional RepositoryCitation: Khan, S. ORCID: 0000-0001-5589-6914 and Abdullah, F. (1993). Finite element modelling of electrostatic fields in process tomography capacitive electrode systems for flow response evaluation. IEEE Transactions on Magnetics, 29(6), pp. 2437-2440. doi: 10.1109/20.280991 This is the accepted version of the paper. This version of the publication may differ from the final published version. Permanent repository link:  https://openaccess.city.ac.uk/id/eprint/23735/Link to published version: http://dx.doi.org/10.1109/20.280991Copyright and reuse: City Research Online aims to make research outputs of City, University of London available to a wider audience. Copyright and Moral Rights remain with the author(s) and/or copyright holders. URLs from City Research Online may be freely distributed and linked to.City Research Online:            http://openaccess.city.ac.uk/            publications@city.ac.ukCity Research OnlineIEEE TRANSACTIONS ON MAGNETICS, VOL. 29, NO. 6 ,  NOVEMBER 1993 2437 Finite Element Modellin of Electrostatic Fields in Process Tomography Capacitive Electro 8 e Systems for Flow Response Evaluation S. H. Khan, Member, IEEE , and F. Abdullah City University, Department of Electrical, Electronic & Information Engineering Northampton Square, London EClV OHB, UK Abstract-This paper describes various aspects and results of 2D finite element (FE) modelling of electrostatic fields in 12-electrode capacitive systems for two-phase flow imaging. The capacitive technique relies on changes in capacitances between electrodes (mounted on the outer surface of the flow pipe) due to the change in permittivities of flow components. The measured capacitances between various electrode pairs and the field computation data are used to reconstruct the cross sectional image of the flow components. FE modelling of the electric field is necessary to optimize design variables and evaluate the system response to various flow regimes, likely to be encountered in practice. Results are presented in terms of normalized capacitances for various flow regimes. The effects of key geometric parameters of the electrode system are also presented and analyzed. I. INTRODUCTION In recent years capacitive technique which forms the basis of electrical capacitive tomography (ECT) for imaging and measurement of two-phase flows has gained considerable momentum [l], [2]. The technique involves a number of capacitive electrodes mounted circumferentially around a flow pipe and interrogated in turn by electronic control. Capacitances are measured between various electrode pairs and the data, thus obtained are used to reconstruct the cross sectional image of flow components. Beck et al. [3] first proposed to exploit this technique which has been found to have considerable potential to be used in process industry, especially the oil industry. Hence, the term ‘process tomography’ has emerged. Recently, sussessful testing of the industrial prototype of a 12-electrode capacitive system [4] has shown the feasibility of this technique for imaging two-phase flows of different permittivities (e. g. oil/gas, oil/water, etc.) in real time. Comparing to other imaging systems capacitive systems are cheap, fast, noninvasive and simple to construct. The quality of the reconstructed image and the performance of a multielectrode ECT system depend on the uniformity of sensitivity distribution between sensor electrodes which, in turn depends on the inherently nonuniform electric field distribution over the flow pipe cross section. This nonuniformity not only depends upon the geometric and material parameters of the electrode system [5] but also upon the permittivities, distributions and orientations of flow components over the flow pipe cross section. For this reason it is important to be able to investigate the effects of various geometric parameters and flow regimes in order to optimize the electrode system and Manuscript received February IS, 1993 achieve best system performance in terms of image quality. This is effectively done for a 12-electrode capacitive system by numerical modelling of electric fields by the finite element method (FEM) [6]. 11. CONSI’RUcnvE FEATURES AND THE WORKING PRINCIPLE OF A MULTIELECIRODE CAPACITIVE SYSTEM Fig. 1 shows the cross section of a 12-electrode capacitive system for ECT flow imaging. It consists of 12 capacitive electrodes mounted symmetrically on the insulating section of a pipeline. The radial screens in between electrodes reduce large capacitances between adjacent electrodes and thereby, increase measurement accuracy. The outer screen with radius R3 is earthed to shield the electrode system from stray fields. The empty space between this screen and the pipe wall outer surface is filled with dielectric material (E = efil) which insulates the electrodes from the screen. The inner radius Ri of the pipe wall ( E  = epw) is usually fEed for a given pipeline. The rest of the geometric and material parameters like the electrode angle 6, pipe wall thickness 81 = R2-R1, outer screen distance 82, radial screen thickness scth, its depth scgp, number of electrodes N, and permittivities ~ f i i  and cPW can vary. Fi 1. Cross section of a Fig. 2. Finite element model of 12g-klectrode capacitive system for the 12electrode capacitive ECT flow imaging (not in scale). The data acquisition in the above system is carried out by imposing a constant potential to one of the electrodes (‘active electrode’) and measuring the capacitances between this and rest of the electrodes (‘detecting electrodes’, kept at zero potential) by discharging the active electrode and measuring the discharging currents (proportional to the unknown capacitances) from the detecting electrodes [l]. For all possible combinations of active and detecting electrodes this process gives a total of n = N(N-1)/2 independent capacitance measurements in an N-electrode ECT system. In between a pair of active and detecting electrodes a narrow region of positive sensitivity can be defined within which a unit dielectric increase leads to an increase in their capacitance measurements. The presence of a dielectric material inside this region can thus be detected from measured capacitances. For all different system (full model). 0018-9464/93$03.00 0 1993 IEEE 2438 combinations of electrode pairs these narrow regions create the total positive sensing area of the electrode system over the pipeline cross section. A suitable image reconstruction algorithm could be used to exploit the functional relationship between the measured capacitances, dielectric and sensitivity distribution functions and solve the inverse problem of determining the actual flow component distribution [2]. I I I . R m  ELEMENT MODELUNG OF ELECTRIC FIELDS IN MULXXZECIRODE CAPACITIVE SYSreMS The electrostatic field in a multielectrode capacitive system shown in Fig. 1 is generated by the active electrode, and the interaction of the field with the dielectric flow components is detected through respective capacitance changes between various electrode pairs. Under corresponding assumptions this field is given by the following Laplace’s equation (considering free charge distribution) in terms of electrostatic potential Q, = @(x, y) in the 2D region Q of a capacitive electrode system. Assumptions: (a) The effects of fringing fields due to the finite length of electrodes are negligible; (b) within the electrode length flow component distribution of a two-phase flow does not change spatially along the axial direction of the pipeline; (c) permittivities of flow components remain constant and do not depend on the field; (d) the dielectric medium in the 2D region $2 is piece-wise homogeneous and isotropic. Under these assumptions and appropriate boundary conditions the 2D FE solution of (1) for given permittivity distributions of flow components E = E(& y) gives the electrostatic potential at any point in the region of interest a. From this field vectors E, D and capacitances between the electrodes are calculated. This capacitance C is calculated from the total charge Q distriiuted on the detecting electrode using C = QN, where V is the potential difference between the electrodes. The total charge Q is obtained using the Gauss’s law [A given by the following equation: (2) VMX, Y) v W X ,  Y)l = 0 in Q (X, Y)EQ (1) Q = JsDn ds = JsDcod ds = .fsD.n ds = J6sD.d~ From equation (2) it follows that the integral of the normal component of the flux density D n  over any closed surface s enclosing the detecting electrode is equal to the total charge Q distributed on it. If the detecting electrode surface is selected as the surface s then the calculation of Q becomes much easier to perform as there is no need to find D n  since electric field lines are always perpendicular to a conducting surface. In this case Q=JsD ds which gives C = (JD ds)/V, where D is the magnitude of vector D. Fig. 2 shows the typical FE model of the electrode system shown in Fig. 1. For this full model, only Dirichlet boundary conditions are used. Specifically, electrode 1 is taken as the active electrode with potential @=Cpi+O. Rest of the electrodes and the outer screen are kept at zero potential (Q,=O). Basically, this model is used to simulate electric fields for various two-phase flow regimes shown schematidy in Fig. 3. Flow concentrationa @ (expressed in %) is given by the ratio of the cross sectional area of the higher permittivity (a) component, S2 and that of the flow pipe, Si; namelyp= (SZlSi)lOO%, where Si =xRi2. For the Fi 3 Various two-phase flow regimes likely to be encountered in p&i& exploitation of capacitive electrode systems: a) core flow b) annular flow c) stratified flow, empty pipe and radially symmetrical flow regimes (e.g. core flow, annular flow) electric field distribution inside the flow pipe is symmetrical as shown in Fig. 4. In these cases only a half model of the electrode system with appropriate Fi 4 Eguipotential lines in an Fi 5. FE model of the 8&c&de capacitive system 12&e!ectrpae capautm system showins. ?metry). in their considmng dstribu ion core flow distributions (=:%elf fie’d boundary conditions (both Dirichlet and Neumann conditions),needs to be considered (Fig. 5). By adding FE regions with appropriate material properties inside the flow pipe FE models for various flow regimes and concentrations are obtained from the basic models shown in Fig. 2 and 5. Figure 6 shows the FE models for (a) 10% pig. 6. FE models for the simulation of various flow regimes: (a) 10% core flow (b) 90% annular flow (c) 21% stratified flow. core @=lo%), (b) 90% annular and (c) 21% stratitied flows, By interchanging the material properties of corresponding FE regions various models for annular flow regimes are obtained from those used for core flows. For stratified flows the orientation of the higer permittivity flow component distribution can be different with respect to a given active electrode. IV.RESULTS AND DISCUSSIONS Fig. 7 shows some of the modelling results for various 2439 flow regimes discussed above. Results are given in terms of the variation of normalized capacitances with flow concentration /I and geometric parameters 61 and scgp. Normalized capacit ce c“ij between electrode pair i-j is ij are capaatances between i-j when the flow pipe is empty @ =0, E =e1 = I), full of material of E =e2 @ = 100%) d$d a~ dij.=(C!$Qij)l(eij-Qij) where, G j ,  d j  and (a) con flow, &=s mm; scgp in mm. m 30 60 70 00 m 50 60 70 90 10 30 w 70 90 FLOW CONCENTRATION, 6 % (b) core flow, &=U, mm; scgp in mm. 10 50 BO 10 50 90 10 50 90 IO 50 90 10 60 90 10 60 90 FLOW CONCENTRATION, 6 % 10 30 60 70 90 XI SO SO 70 00 10 30 60 70 00 FLOW CONCENTRATION, @ % z P 0 2 2  3 ’  B - I  (d) annular flow, 61 = 20 8 o mm; scgp in mm. 2 3 -’ (Q W 90 10 80 00 10 60 00 10 60 90 10 60 90 10 60 90 FLOW CONCENTRATION, @ % stratifie flow, = 2 mm; 81 in mm. FLOW CONCENTRATION. @ % Fig. 7. Effects pipe wall thickness 61 radial screen depth scgp and flow concentration $on normalized capacitajnces. and has a two-phase flow of given concentration # b o  (q = 1, e2> 1) respectively. Normalized capacitance is one of the main performance parameters of capacitive electrode systems. To avoid saturation of sensor electronics due to large capacitance changes and ensure good quality image reconstruction it is desirable to limit the values of these capacitances SO that 0 S C “ i j S l  [2]. Fig. 7 clearly reflects the effects of flow regimes and concentrations @) and the geometric parameters of the electrode system (SI, scgp) on normalized capacitances which, eventually determine the image quality. For thin pipe wall electrode systems (Fig. 7% c and e) these capacitances mostly remain between 0 and 1 (especially for core and annular flows) and do not depend on and scgp. However, for thick pipe wall electrode systems with small scgp (Fig. 7b, d and e) large ca acitances are observed between adjacent electrodes evident in the case of stratified flows (Fii. 7e) for which even larger C“112 have been obtained for some orientations of the higher permittivity flow component [8]. As can be seen from Fig. 7b and d, for a given 61, high normalized capacitances between adjacent electrodes can be reduced by appropriately choosing the radial screen depth scgp. V. CONCLUSIONS C lP 112 (electrode 1 is the active electrode). This is especially One of the vital performance parameters of a 12-electrode capacitive system for ECT flow imaging has been investigated by FE modelling of electric fields. Various results have shown the effectiveness of the adopted modelling approach (validated by experiments [9]) for the CAD and performance evaluation of these systems. ACKNOWLEDGMENT The authors would like to thank SERC, UK for financing this work under an SERC grant, Professor M. S. Beck and Dr. C. G. Xie from UMIST and Dr. S. M. Huang from the Schlumberger Cambridge Research Limited, UK for their long standing collaboration. REPERENCES [l] S. M. Huang, C. G. Xie, R Thom, D. Snowden, and M. S. Beck, “Design of sensor electronics for electrical capacitance tomography,” IEE Pmmdngs-G, vol. 139, no. 1, pp. 8388,1992. [2] C. G. Xie, S. M. Huang, B. S. Hoyle, R Thom, C. Lenn, D. Snowden, and M. S. Beck, “ElectriCal capacitance tomography for flow imaging. system model for development of image reconstruction and design of primaly sensors,” IEE Pmcedhgs-G, vol. 139, no. 1, pp. 8948,1992. [3] M. S. Beck, A. Plaskowski, and R G. Green, “Imaging for measurement of two-phase flows,” in VERET, C. (Ed.): How Visualization IV, Proc 4th Int Symposlnm on Flow Visualiza&n, [4] M. S. Beck, B. S. Hoyle, and C. P. Lenn, ‘‘Process tomography in pipelines,” SERC Bulletin, vol. 4, no. 10, pp. 24-25,1992. [SI S. H. Khan and F. Abdullah, ”Computer aided design of p’ocess tomography capacitance electrode systems for flow imaging,” in Sensors: Technology, systems and Applications, Ed. K T. V. Grattan, Bristok Adam Hilger, 1991, pp. 209-214. [6] P. P. Sihrcster and R L Ferrari, Finite Elements for Electrical Engineers, 2nd ed., Cambridge: Cambridge University Press, 1990. [I S. Ramo, J. R Whinnery, and T. V. Duzer, Fields and Waves in Communicntion Electronics, New York John Wiley & Sons, Inc., [SI S. Umashangar, “A study of the system response to stratified flow for a 12clectrode flow imaging system using finite element method,” B.Eng Project Report, City University, London, 1992. [9] S. H. Khan and F. Abdullah, Validation of finite element modelling of multielectrode capacitive system for process tomography flow imaging,” in Proc E m p .  COncerM Action on Profess Tomography, Manchester, March 1992, pp. 29-39. pp. sss-sss,1986. 1965, p. 754. 

Finite element modelling of electrostatic fields in process tomography capacitive electrode systems for flow response evaluation

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Finite element modelling of electrostatic fields in process tomography capacitive electrode systems for flow response evaluation

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