Investigation of Complex Permittivity/Conductivity Distribution by Electrical Tomography

Electrical tomography techniques have been investigated extensively in the last decade, for both industrial and medical applications. There are three modalities: electrical resistance tomography (ERT), electrical capacitance tomography (ECT) and electromagnetic tomography (EMT), which provide conductivity, permittivity and permeability distributions, respectively. Electrical tomography has several advantages over other tomographic techniques, e.g. low-cost, rapid response, portability, no radiation hazard and robustness. In the industrial area, electrical tomography has found many applications, e.g. measurement of gas/liquid and gas/solids flows in pipelines, analysis of dynamic processes in fluidized beds, monitoring of mixing and separation processes, visualization of combustion flames in engine cylinders and detection of leakage from buried water pipes. In the medical area, it has been used to image swallowing, stomach emptying, lung ventilation and perfusion, pulmonary oedema, brain function and breast tumours.Compared with `hard-field' tomographic techniques, such as x-ray, the main difficulty with electrical tomography is that the relationship between the electrical measurements and the material properties is highly nonlinear, as the sensing fieldis distorted by objects in the imaging area. Therefore, the `soft field' nature presents particular difficulties in image reconstruction. Currently, linear back-projection (LBP) algorithms are commonly used in electrical tomography systems. They are simple and fast, but can only produce qualitative images and hence are unsuitable for quantitative analysis. In recent years, iterative image reconstruction algorithms have been developed to address the nonlinearity and ill-posed challenges. Although there exist many different iterative algorithms, their basic principles are the same. In essence, resistance, capacitance or inductance is calculated from the current image using a forward problem solver. The difference between the calculated values and the real measurements is used to correct the image, aiming to reduce the error. In general, iterative algorithms produce improved images, but they can only be used off-line because they are slow. However, with ever-increasing computer speed, real-time iterative image reconstruction should be feasible in the near future.There are many similarities between ERT, ECT and EMT systems. In terms of physics, the three sensing fields are governed by the same Laplace equation. In hardware, most systems are based on low-frequency (<1 MHz) sinusoidal excitation and phase-sensitive demodulation, although ERT and EMT systems often employ current injection excitation and ECT systems apply voltage excitation. In software, all three types face the same difficulties, i.e. nonlinearity and ill-posed problems, and all of them use finite element or finite difference methods to solve the Laplace equation. Considering the above common aspects, it is possible to develop a universal electrical tomography system, which can perform ERT, ECT and EMT. By integrating the three modalities onto a single platform, the common problems may be solved together. In addition, such a system may find wide applications, such as measuring three-component flows.Some differences do exist between the two application areas. In industrial applications, the geometry is fixed and regular, electrical properties are often known and the dynamic range can be large. In medical applications, however, the geometry is irregular and may be changing, electrical properties are not well documented and the dynamic range is small. Although safety issues are equally important to both application areas, they have received more attention for medical applications than industrial applications so far.In 1996, a Special Issue on Process Tomography was published by Measurement Science and Technology, and it was well received by researchers working on industrial tomography. This Special Feature focuses on electrical tomography. The main aim is to bring the industrial and medical issues together and to provide readers with a comprehensive review of the state-of-the-art of electrical tomography technology. The papers come from 12 countries and cover a wide range of applications. Accordingly, most papers are concerned with application-specific researchrather than general principles. This may indicate that electrical tomography is close to its real application stage. The papers have been arranged in four categories: ERT, ECT, EMT and multi-modality.As Guest Editor of this Special Feature, I would like to thank the journal Editors Dr Sharon D'Souza, Mr James Dimond and Professor Richard Dewhurst for their help and efficient work. I would also thank all the authors and the referees for their effort to make this Special Feature possible.

Because of the ‘soft-field’ nature, all electrical tomography sensors suffer from electric field distortion, i.e. the fringe effect. In electrical resistance tomography (ERT) sensors, small pin electrodes are commonly used. It is well known that the pin electrodes result in severe electric field distortion or the fringe effect, and the sensing region of such an ERT sensor spreads out of the pin electrode plane to a large volume. This is also true for electrical capacitance tomography (ECT) sensors, even though it is less severe because of larger electrodes and grounded end guards used. However, when the length of electrodes in an ECT sensor without guards is reduced to almost the same dimension as those in an ERT sensor, the fringe effect is equally obvious. To investigate the fringe effect of ERT and ECT sensors with and without guards, simulations were carried out with different length of electrodes and the results are compared with the corresponding 2D simulation. It is concluded that ECT and ERT sensors with longer electrodes have less fringe effect. Because grounded end guards are effective in reducing the fringe effect of ECT sensors, we propose to apply grounded guards in ERT sensors and integrate ECT and ERT sensors together. Simulation results reveal that ERT sensors with grounded guards have less fringe effect. While commonly current excitation is used with ERT sensors, we propose voltage excitation instead to apply the grounded guards. The feasibility of this approach has been verified by experiment. Finally, a common structure for reducing the fringe effect is proposed for ECT and ERT sensors for the first time to simplify the sensor structure and reduce the mutual interference in ECT/ERT dual-modality measurements.

A dual-modality electrical tomography sensor for measurement of gas–oil–water stratified flows

Fuzzy clustering based ET image fusion

In electrical resistance tomography (ERT) sensors, small pin electrodes are commonly used. It is well known that the pin electrodes cause severe field distortions or 3D effect, and the sensing region of such an ERT sensor is not constrained to the pin electrode plane, but spreads to a large volume. This is also true for electrical capacitance tomography (ECT) sensors, even though it is less severe because of larger size electrodes in ECT sensors. However, when the length of electrodes in an ECT sensor is reduced to almost the same dimension as those in ERT sensor, the 3D effect may be equally obvious. To investigate the 3D effect of ERT and ECT sensors, simulation was carried out with different lengths of electrodes and the results are compared with the corresponding 2D simulation. It is concluded that sensors with longer electrodes usually have less 3D effect without guard electrodes. To investigate the effectiveness of grounded guards, 3D simulation was carried out for ECT sensors with grounded guards and the results are compared with the previous results in term of the 3D effect. It is found that the 3D effects of ECT and ERT sensors without guards are similar to each other, and the grounded guards can reduce the 3D effect of ECT sensors to a great extent.

This paper reports a new approach to quantitatively evaluate the performance of Electrical Tomography (ET) in measuring dynamic multiphase flows. A virtual multiphase flow imaging platform based on ET is constructed and demonstrated on two typical gas–liquid flows, i.e., water–gas flow and oil–gas flow. Two coupling simulation cases, i.e., water–gas flow field and electric currents field coupling simulation and oil–gas flow field and electrostatics field coupling simulation, are performed to simulate multiphase flow sensing of Electrical Impedance Tomography (EIT) and Electrical Capacitance Tomography (ECT). We quantitatively evaluated the representative EIT and ECT image reconstruction algorithms on the virtual evaluation platform bringing evidence of the improved capability to capture the key flow features of the fluid mixture with respect to traditional static phantoms. Ad-hoc treatment of the signal noise enables one to better capture dynamic responses of the fluid phase volume fractions and their spatial gradients throughout their mixing along the conduit, ultimately demonstrating unprecedented potential in the quantitative characterization of complex, unsteady multi-phase systems. The proposed image reconstruction constitutes a highly effective platform for quantitative performance evaluation of ET, parameter optimization of model-based ET image reconstruction algorithms, and for the development of data-driven ET algorithms in multiphase flow imaging.

Electrical Tomography technology is widely used in the research and engineering practice of two-phase flow due to its advantages of non-radiation, non-intrusive and simple equipment structure. However, because of the electrical tomography sensitive field distribution of medium nonlinear (soft), the reconstructed images are often distorted, especially when faced with high conductivity and high dielectric constant two-phase flow (such as oil-field water of high salinity). Displacement current phase tomography (DCPT) is a new electrical tomography technology and it is proposed in 2017. An attractive feature of DCPT is that the relationship between the measured phase and the loss factor has a more extended linear range than the relationship between the measured capacitances in ECT and the permittivity distribution. In this paper, a 12-electrod DCPT with Landweber reconstruction algorithm is applied for gas-water two-phase flow imaging, and the reconstruction results are compared with electrical capacitance tomography (ECT) by numerical examples.

Electrical capacitance tomography (ECT) and electrical resistance tomography (ERT) have been developed separately as non-intrusive and/or non-invasive imaging techniques in the past. One of their applications is to measure multi-phase flows. The conventional ECT and ERT modalities are implemented individually. While ECT can be used to visualise permittivity distributions and ERT to visualise conductivity distributions, in many cases a material distribution cannot be described simply by a permittivity or conductivity distribution, but a combination of permittivity and conductivity. While it has been attempted to develop an ECT/ERT dual modality system, an ECT sensor and an ERT sensor are used separately. This paper presents an integrated ECT/ERT dual-modality sensor with 8 capacitance electrodes and 8 resistance electrodes. To evaluate the performance of the integrated ECT/ERT sensor, simulations were carried out using COMSOL. It has also been tested using a data acquisition system with an impedance analyser (HP4192A), which can take capacitance and resistance measurements simultaneously. From the measurements, a permittivity distribution and a conductivity distribution can be generated for the same location. Experiments results are given for imaging gas-oil, gas-water, and gas-milk two-phase distributions and gas-oil-water three-component distributions.

For some applications, it is necessary to visualize an industrial process by both electrical capacitance tomography (ECT) and electrical resistance tomography (ERT). For this purpose, dual-modality ECT/ERT has been developed. A major challenge in this task is the constant changing of electrical property, from predominantly conductive to mainly dielectric. The current ERT systems do not perform as well as ECT systems, limiting the integration of ECT and ERT to be a dual- modality system. In this work, the use of voltage-excitation for ERT and a 4-wire sensor structure allows effective fusion of ERT and ECT in a single set of electrodes to measure capacitance and conductance simultaneously in a spatially and temporally coherent way.

Multiphase flow is ubiquitous in nature, industry and research, and accurate flow imaging is critical to understanding this complex phenomenon. Electrical tomography (ET) is a promising technique for multiphase flow visualization and characterization which provides a non-invasive and non-radiative way to unravel the internal physical properties at high temporal resolution. However, existing ET-based multiphase flow imaging methods are inadequate for quantitative imaging of multiphase flows due to inversion errors and limited ground truth data of fluid phases distribution. Here we report a digital twin (DT) framework of ET to address the challenges of real-time quantitative multiphase flow imaging. The proposed DT framework, building upon a synergistic integration of 3D field coupling simulation, model-based deep learning, and edge computing, allows ET to dynamically learn the flow features in the virtual space and implement the model in the physical system, thus providing excellent resolution and accuracy. The proposed DT framework is demonstrated using electrical capacitance tomography (ECT) of a gas-liquid two-phase flow. It can be readily extended to a broader range of tomography modalities, scenarios, and scales in biomedical, energy, and aerospace applications.

Electrical tomography for characterizing transport properties in cement-based materials: A review

Among electrical tomography techniques, electrical capacitance tomography (ECT) has been the subject of extensive recent research due to its non intrusive and non-invasive nature. It is used for obtaining information about the distribution of the contents of closed pipes or vessels by measuring variations in the dielectric properties of the material inside the vessel. An experimental study was conducted by producing two-phase bubble flow regime in a vertical online ECT column. This experimental study measures the void fraction in a two-phase bubble flow regime by using ECT and differential pressure (ΔP). Differential pressure is also a simple and reliable approach. The experiments conducted for this study used compressed air as the gas phase and deionised water as a liquid phase. On the variation in superficial gas velocity from 0.0021 to 0.03 m/sec, and superficial liquid velocity from 0 to 0.034 m/sec, some different kinds of sub-bubble flow regimes were observed within the column. The experimental results show the influence of gas velocity on the void fraction in an increasing manner. The raw data obtained from ECT was also compared with the simulated data which shows a good agreement to each other.

CGAN-ECT: Reconstruction of Electrical Capacitance Tomography images from capacitance measurements using Conditional Generative Adversarial Networks

Chapter 5 Electrical Capacitance, Electrical Resistance, and Positron Emission Tomography Techniques and Their Applications in Multi-Phase Flow Systems

Electrical tomography systems are imaging based measurement systems, which draw information about an inner state of an object from electrical impedance systems. Among them are electrical impedance tomography, electrical capacitance tomography or electrical resistance tomography. For imaging reconstruction a highly dimensional, ill-posed inverse problem has to be solved. Back-projection type reconstruction methods mark a class of algorithms of low computational complexity. Still, the high dimensionality causes restrictions with respect to the quality and the robustness of these methods. In this work we show the incorporation of a state reduction technique to reduce the high dimensional state vector within different backprojection type reconstruction methods. We demonstrate the usefulness of this approach e.g. with respect to its enhanced robustness and show its application for measurements in non-stationary industrial flow monitoring.