paraphrase

ECT System

Electrical Capacitive tomography is used to find the permittivity distribution of the material within an area; it is successfully employed to image the flow in pipes. An ECT sensor consists of pair of Electrodes surrounding the region where permittivity distribution needs to be found. A Schematic diagram of the capacitances measurement system is given below:

Figure 1 Complete ECT System [3]

The ECT system consists of system of measurement Electrodes that are known as sensors, these electrodes are excited by applying a potential on one electrode, whereas the rest of the electrode are grounded. The measurement system finds the capacitance between each excited electrode and the remaining electrode. It has already been outlined that there are N (N-1)/2, independent measurements possible with N electrodes [1]. Permittivity distribution is estimated from the measurements of the capacitance between the electrodes. It is therefore necessary to accurately model the influence of the permittivity distribution inside the ECT sensor on the measured capacitances to reach reliable estimations. The sensitivity matrix links the signal variation on one electrode to the permittivity variation in a given volume element inside the ECT sensing domain.

Figure 2 ECT Sensor with 04 Electrodes showing inter-electrode Capacitance

The Concept of sensitivity matrix and the approaches used to estimate it are of importance in finding the permittivity map or image of the sensing domain. The approached used to compute the sensitivity map would be discussed briefly in this report; however the major aim of this report is to discuss the design of the ECT sensor. The architecture of the ECT sensor is discussed along with the major components and purpose of the each of the each of the sensor. This report the simulation results to find the potential distribution within the sensing domain would be discussed along with the experimental results that are provided in the references and various approaches which are used to optimize different parameters are discussed.

ECT Sensor Architecture

Capacitance between the two electrodes depends on the effective area of the electrode and the permittivity of the medium in the sensing domain. In order to have larger capacitance it is desired that the area of the electrode be large, whereas if the area of electrode increases the spatial resolution decreases [2]. On the other hand area of the electrode cannot be decreased beyond a certain limit sine capacitance measured within the sensing domain has a variation of about 0.01pF and it poses some limitation on the measurement system since reducing the area of electrode decreases the signal hence it becomes difficult to measure the small capacitances. The figure below show the major components of the ECT Sensor

Figure 3 ECT Sensor System [2]

The ECT sensor has three different types of electrodes; main electrodes are used for capacitance measurement, axial electrodes and radial electrodes are referred to as guard electrodes. The purpose of the axial electrode is to reduce the coupling between the neighboring electrodes, whereas the radial electrodes are incorporated to reduce the 3-D fringing effect of the field. The radial electrodes, axial electrodes and the screen which encloses all the assembly are grounded. The outer screen is grounded so that the effect of interference from outside environment is minimum. The sensor assembly is usually mounted on the pipe which is made up of some dielectric material such as PVC. The capacitance between the electrode and screen is usually much higher than the inter-electrode capacitance being measured, the capacitance between the electrode and screen and axial guards is of the order of the 150 pF, whereas the capacitance variation in the sensing domain is usually of the order of 0.1-0.01pF. There the design parameters of the ECT which need to be optimized are [2]:

1. Thickness and the material of the wall between the electrodes and the sensing domain.

2. Thickness and the material of the wall between the electrodes and the screen.

3. Size of the electrode.

4. The effect of the Radial or plane axial guards.

5. Spacing between the electrodes and the guards, and the size of the guard electrodes.

The 3D fringing effect of the field can be reduced by using the electrode that are longer length, however it would reduce the axial resolution since most of the time material distribution in the sensing domain is constant. Therefore in order to have a good axial resolution some time driven guard electrodes are used. The use of the driven guard electrodes as is shown in the figure would enable the designer to keep the axial length of the electrodes smaller, however the driven guard would introduce its own field effect that are not easy to decouple and hence it would perturb the overall measurement of the capacitance.

Figure 4 Driven Guard Electrodes [2]

In order to reduce the field fringing effect usually the length of the electrode is kept equal to the diameter of the pipe of the sensing domain. Simulations are performed in Computational Electromagnetics based software to investigate the effect of Radial guards and the effect of grounding; these simulations later were verified by actual measurements.

Sensitivity matrix based analysis is also performed in commercial CEM software such as COMSOL to investigate the effect of different electrodes couplings. In using this software care is taken to apply the appropriate EM boundary conditions and computational domain is discretized using very fine grid. In many situation at first 2D simulations are performed to optimize radial dimensions of the sensor and later 3D simulations are performed to take into account axial length effects and optimization of the axial parameters of the sensor. Research is still in its initial phases and the ECT technology is only successfully applied for flow measurements and for applications where high acquisition speed is required rather than high resolution, since one of the current research endeavor in ECT is to increase the resolution by designing optimum sensor.

Effect of the Radial Guards

The effect of different guard electrode on the potential distribution within the computational domain is investigated with different media between the sensing electrodes and the external screen. The three different configurations were simulated, one without any guard electrode, then another configuration was with axial guard and the last one was with the radial guard. These configurations are shown in figure [2]:

Figure 5 Three Electrode configurations [2] (a) Without guard (b) With Axial guard (c) With Radial guard

The potential distribution is plotted when electrode number one was excited with 10 volts and the rest of the electrode were held at ground potential. The standing capacitance was computed for all of these configurations. The capacitance is also measured for different screen distances and for various permittivity values between screen and sensing electrodes, the results of which are:

Figure 6 Effect of Guard on Standing Capacitance [2]

In the above simulation the sensing zone is assumed to be filled with air, having relative permittivity of 1, whereas the area between electrode and screen is filled with medium having relative permittivity of 3.0. The simulations show that capacitance without any guard electrode is strongly affected by the distance between the electrodes and screen, whereas the capacitance is least effected by the distance in case when radial guard are used. Similarly simulations were also performed by taking into account different medium between sensing electrode and the screen and results were also similar to the previous simulation. The capacitance almost become independent of the material when we use the radial guard and in absence of any guard the capacitance is a strong function of the medium as is shown in figure:

Figure 7 Standing Capacitance dependence on Medium for different [2] Guarding Schemes

The above simulations results are very important in the sense that they indicate that guarding scheme would reduce the standing capacitance; hence it would make the measurement of capacitance within the sensing domain easier as the standing capacitance is usually very large as compared to capacitance variation being sensed by the measurement system. In ECT systems usually normalized capacitance is measured by first filling the sensing domain by the low permittivity material such as air and afterword filling the domain by high permittivity medium. This procedure removes the systematic error in the measurement performed. The normalized capacitance [2] is defined as:

Effect of the coupling between the capacitance within the sensing domain and the screen was studied by plotting the normalized capacitance with and without the guard. The results obtained for nominal permittivity variation from 1-3 shows that coupling is not significant; however large standing capacitance poses measurement difficulties.

Figure 8 Effect of Coupling on Normalized Capacitance [2]

Simulation Results for the 3-D Effects

The previous simulations were performed taking into account the only the 2-D configuration of the 12 sensors. When simulation are performed for 3D sensor as is shown in the figure the difference between the capacitance measured is significant for the medium in the sensing domain having higher permittivity.

Figure 9 2D and 3D Geometry for Modeling ECT Sensor

Figure 10 Capacitance Measured for 2D and 3D Case[2]

Experimental Verification:

The capacitance was measured for the case when the sensor was empty and when the sensor was filled with a medium having permittivity of 1.7. The results of the measured and simulated are plotted, also results of the percentage error are also plotted. The results show good agreement between the simulated and measured results, however there is about 10% variation in the measured results which can be attributed to the following factors:

1. Modeling error due to difference between actual measurement setup and simulated configuration

2. Soft field effects

3. Interference

4. Instrument errors

5. Numerical error

Figure 11 Measured and Simulated Results[2]

Figure 12 Percentage error in Capacitance between simulated and Experimental results[2]

Conclusions:

Simulation investigated the effect of the medium permittivity on Capacitance and simulated the effect of standing capacitance. It was demonstrated that standing capacitance can be made smaller by using axial and radial guards. The guards not only reduce the standing capacitance but also reduce the dependence on other parameters making the capacitance measurement much more tractable.

Sensitivity Matrix

Inter electrode Capacitance that is measured for each pair of electrode, by exciting an electrode with a known voltage and keeping all other electrodes at ground potential, is strongly dependent of the permittivity distribution in the sensing domain [1].

Sensitivity matrix relates the measured capacitances with the permittivity distribution within the sensing domain. The inter electrode capacitances for a 12 electrode system are 66 different measurements are available. Since capacitance is dependent on the permittivity distribution in the sensing domain we h have,

If permittivity is changing therefore capacitance would also change, therefore it can be derived for a very small variation in permittivity the capacitance variation are given by:

Here in the above equation the derivative provide how capacitance is perturb by a small variation in the permittivity, hence it represents the sensitivity to capacitance by permittivity of the medium in the sensing domain. Neglecting the higher order terms we can write,

In order to visualize the permittivity distribution the sensing domain is discretized, for example if we want to image 1024 pixels in the sensing domain it can be discretized into 32*32 grids.

The discrete formulation is given by:

Here is the capacitances measured, for a 12 electrode system there are 66 measurments available for a 1024 pixel or grid points I the sensing domain is having 1024 unknowns, whereas the sensitivity matrix J, which is the Jacobian is also known as the sensitivity distribution matrix[1].

Since the numbers of unknowns, which are the 1024 permittivity in this case, are much larger than the number of capacitance measurements, for 12 electrode sensor there are 66 measurements available, therefore it is under determined problem. It is also an ill posed problem since the relationship between capacitance and permittivity is not linear and hence can’t be linearized.

References:

1. W. Yang and L. Peng, “Image reconstruction algorithms for electrical capacitance tomography,” Meas. Sci. Technol., vol. 14, pp. R1–R13, 2003.

2. Alme, K.-J.; Mylvaganam, S., "Electrical Capacitance Tomography &Sensor Models, Design, Simulations, and Experimental Verification," Sensors Journal, IEEE , vol.6, no.5, pp.1256,1266, Oct. 2006

3. Zhaoyan Fan and Robert X Gao, “A frequency selection scheme for increased imaging speed in ECT” 2013 Meas. Sci. Technol. 24 074009