Electrical capacitance tomography (ECT) is used to image cross-sections of industrial processes containing dielectric material. This technique has been under development for more than a decade. The task of image reconstruction for ECT is to determine the permittivity distribution and hence material distribution over the cross-section from capacitance measurements. There are three principal difficulties with image reconstruction for ECT: (1) the relationship between the permittivity distribution and capacitance is non-linear and the electric field is distorted by the material present, the so-called 'soft-field' effect; (2) the number of independent measurements is limited, leading to an under-determined problem and (3) the inverse problem is ill posed and ill conditioned, making the solution sensitive to measurement errors and noise. Regularization methods are needed to treat this ill-posedness. This paper reviews existing image reconstruction algorithms for ECT, including linear back-projection, singular value decomposition, Tikhonov regularization, Newton–Raphson, iterative Tikhonov, the steepest descent method, Landweber iteration, the conjugate gradient method, algebraic reconstruction techniques, simultaneous iterative reconstruction techniques and model-based reconstruction. Some of these algorithms are examined by simulation and experiment for typical permittivity distributions. Future developments in image reconstruction for ECT are discussed.

https://iopscience.iop.org/article/10.1088/0957-0233/14/1/201/pdf

Image reconstruction algorithms for electrical capacitance tomography

Electrical capacitance tomography (ECT) has been developed since the late 1980s for visualization and measurement of a permittivity distribution in a cross section using a multi-electrode capacitance sensor. While the hardware and image reconstruction algorithms for ECT have been published extensively and the topics have been reviewed, few papers have been published to discuss ECT sensors and the design issues, which are crucial for a specific application. This paper will briefly discuss the principles of ECT sensors, but mostly will address key issues for ECT sensor design, with reference to some existing ECT sensors as a good understanding of the key issues would help optimization of the design of ECT sensors. The key issues to be discussed include the number and length of electrodes, the use of external and internal electrodes, implications of wall thickness, earthed screens (including the outer screen, axial end screens and radial screens), driven guard electrodes, dealing with high temperature and high pressure, twin planes for velocity measurement by cross correlation and limitations in sensor diameter. While conventional ECT sensors are circular with the electrodes in a single plane or in twin planes, some non-conventional ECT sensors, such as square, conical and 3D sensors, will also be discussed. As a practical guidance, the procedure to fabricate an ECT sensor will be given. In the end are summary and discussion on future challenges, including re-engineering of ECT sensors.

https://iopscience.iop.org/article/10.1088/0957-0233/21/4/042001/pdf

Design of electrical capacitance tomography sensors

This article reports recent advances and progress in the field of electrical capacitance volume tomography (ECVT). ECVT, developed from the two-dimensional electrical capacitance tomography (ECT), is a promising non-intrusive imaging technology that can provide real-time three-dimensional images of the sensing domain. Images are reconstructed from capacitance measurements acquired by electrodes placed on the outside boundary of the testing vessel. In this article, a review of progress on capacitance sensor design and applications to multi-phase flows is presented. The sensor shape, electrode configuration, and the number of electrodes that comprise three key elements of three-dimensional capacitance sensors are illustrated. The article also highlights applications of ECVT sensors on vessels of various sizes from 1 to 60 inches with complex geometries. Case studies are used to show the capability and validity of ECVT. The studies provide qualitative and quantitative real-time three-dimensional information of the measuring domain under study. Advantages of ECVT render it a favorable tool to be utilized for industrial applications and fundamental multi-phase flow research.

https://www.mdpi.com/1424-8220/10/3/1890/pdf

Electrical capacitance volume tomography: design and applications.

Based on the electrical capacitance tomography technique, a new method for the void fraction measurement of two-phase flow is proposed. A 12-electrode void fraction measurement system is established. A mathematical model of image reconstruction of electrical capacitance tomography is developed. To obtain the quantitative information of two-phase flow, combining the Tikhonov regularization principle and the algebraic reconstruction technique algorithm, a new image reconstruction algorithm is presented. The experimental results show that the accuracy of void fraction measurement is satisfactory. The proposed method is suitable for the void fraction measurement of many kinds of two-phase flow.

Application of electrical capacitance tomography to the void fraction measurement of two-phase flow

UMIST is one of the establishments where process tomography techniques were first developed This paper introduces the development of capacitance tomographic imaging systems at UMIST for oil pipeline measurements The principles of electrical capacitance tomography (ECT) are briefly presented and two ECT systems based on charge/discharge capacitance measuring circuits are described These systems, a PC‐based 8‐electrode system and a Transputer‐based 12‐electrode system, have been used to visualise oil pipelines Future developments of ECT technology are discussed, including a low‐cost PC‐based ECT system, a twin‐plane ECT system which can measure the velocity profile of a pipeline flow, a multi‐frequency ECT system using ac capacitance measuring circuits and an ECT system with a rotating parallel excitation field

Development of capacitance tomographic imaging systems for oil pipeline measurements

For years scientists have been writing horrendously complicated programs to try to simulate on computer screens what they think goes on inside pi pe lines, chemical-mixing vessels and reactors. Their aim was to improve the transport of fluids through pipes and mixing in chemical plants so as to cut costs and increase efficiency. This work has led to new designs of process plants that have saved millions of pounds. Now they can find out if their simulations were right. Members of the UMIST Process Tomography Group describe a tomographic scanning technique which allows them to 'see' through the walls of pipelines and enclosed vessels to monitor the flow of fluids and other materials inside.

Principles and industrial applications of electrical capacitance tomography

The development of stray-immune circuits to measure very small floating capacitances has enabled the technique of electrical capacitance tomography (ECT) to be developed. Burning fuel, for example in an internal combustion engine, produces a high concentration of ions, thus modifying the dielectric constant of the combustion volume. Thus ECT can be applied to produce tomographic images inside a combustion chamber, independent of flame luminosity. However, the major effect of the increase in ion concentration is to increase the conductivity of the volume. The ECT technique has been extended to measure both the change in permittivity and change in conductivity, yielding additional information on the flame composition. Current spatial and temporal resolution is poor but developments are in hand to overcome these limitations. Alternatively, the way forward may well be to abandon images and instead use extremely simple and cheap sensors to monitor knock on a cycle-by-cycle basis. An alternative use of such a simple sensor would be to monitor cycle dispersion in a lean burn engine. Both these techniques could help minimize fuel consumption, whilst maximizing power output and keeping emissions low.

http://iopscience.iop.org/article/10.1088/0957-0233/7/3/018/pdf

Combustion imaging from electrical impedance measurements

First results of engine flame imaging using electrical capacitance tomography (ECT) are described. A six-electrode capacitance sensor fabricated as part of a research engine provides 15 capacitance measurements per scan. A transputer-based ECT system is used to reconstruct the cross-sectional images of flames in the engine from successive sets of capacitance measurements. The prototype system is capable of capturing flame images at 315 frames per second and has potential for monitoring engine performance.

Engine flame imaging using electrical capacitance tomography

Stray-immune circuits are available that will measure very small floating capacitances at high speed These circuits have facilitated the development of Electrical Capacitance Tomography (ECT), which uses fixed, robust metal plates as sensors, arranged non-intrusively around the periphery of the volume of interest. The phenomenon of flame ionization is well understood, with general agreement that the concentration of all the major ions maximize at the flame front. There is also strong experimental evidence to suggest that the presence of carbon particles (and their precursors) results in a large increase in the charge carrying capacity of the flame. This paper reports some initial results from using ECT to visualize the position, size, composition and movement in flames in open and closed combustion chambers.

R. He

Papers

Principles and industrial applications of electrical capacitance tomography

Combustion imaging from electrical impedance measurements

Engine flame imaging using electrical capacitance tomography

Flame visualizations using electrical capacitance tomography (ECT)

Combustion Imaging in Engines Using Electrical Impedance Measurements