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 paper concerns the application of electrical capacitance tomography (ECT) for media of high dielectric permittivity such as water. The performance of an ECT sensor was analysed numerically for a range of dielectric materials (1≤er≤80) and geometrical parameters. On the basis of numerical simulations an ECT sensor with internal electrodes was built. Experimental results concerned with imaging air voids in distilled water and water-continuous dispersions of oil, using a commercially available PTL tomography system, are presented. Effects arising from the conductivity of water are studied and prospects of using the ECT system in an `electrical resistivity' mode for weakly conductive solutions are outlined.

https://iopscience.iop.org/article/10.1088/0957-0233/11/6/318/pdf

The design of an electrical capacitance tomography sensor for use with media of high dielectric permittivity

Electrical Resistance Tomography (ERT) has the capability of offering time-evolving multidimensional comprehensive process knowledge, enrichment of fundamental process understanding and enhancement of the design and operation of process equipment by measuring the conductivity distribution within a process-plant of interest. This paper reviews the wide variety of previous work on ERT applications to Chemical Engineering. The applications are categorized based on the unit operations ERT has been applied to, the media under investigation, the purpose of ERT measurements and also other technologies used in conjunction with ERT. The aim of this taxonomy is to provide the reader with a general understanding of the current situation of ERT related research and proven applications in the Chemical Engineering field and to facilitate the recognition of research gaps for future investigation. Based on this detailed taxonomy and review the potential application of ERT to the milk powder processing industry was identified. Some results of the application of ERT to milk mixing/holding tanks and milk flow pipelines for the purpose of concentration and composition measurements, detection of abnormalities and faults, and multidimensional flow and velocity profile measurements have also been presented as a case study of using this taxonomy.

Electrical Resistance Tomography (ERT) applications to Chemical Engineering

This paper presents the design and geometry optimization of a conductivity probe with a vertical multiple electrode array (VMEA), which can be used to measure the volume fraction and axial velocity of two-phase flow. The designed VMEA electrodes are axially flush mounted on the inside wall of an insulating duct. On the basis of a finite element analysis method, some new sensor optimization concepts of the electric field such as uniform degree, spatial sensitivity and effective information content are proposed. The designed VMEA measurement system has been tested through the multiphase flow loop and shows that the optimized VMEA can be used to measure cross-correlation velocity and predict volume fraction in vertical upward gas–water two-phase flow with satisfactory accuracy. The proposed optimization method of VMEA can also be useful in investigating other types of conductivity probes.

https://iopscience.iop.org/article/10.1088/0957-0233/19/4/045403/pdf

Design and geometry optimization of a conductivity probe with a vertical multiple electrode array for measuring volume fraction and axial velocity of two-phase flow

This paper describes the design and construction of a local six-electrode conductivity probe which can be used in solids-water pipe flows to simultaneously measure the local solids volume fraction and the local solids axial velocity. Using finite element analysis, the probe electrode geometry was designed so that the regions of the solids-water mixture that were interrogated by the probe were optimal for measurement of the volume fraction and for cross correlation velocity measurement. The probe was used, in conjunction with a computer controlled traversing mechanism, to obtain distributions of the local solids volume fraction and the local solids axial velocity both in vertical upward and in upward inclined solids-water flows. Such distributions can be used to validate volume fraction and velocity profiles obtained using dual-plane electrical resistance tomography systems. Experimental results indicated that the six-electrode probe can be used to estimate the local solids volume fraction in vertical upward solids-water flows with a mean absolute error of approximately 0.01. Experimental results also indicated that the six-electrode probe can be used to measure the local axial solids velocity with a mean error of 2% of the reading.

https://iopscience.iop.org/article/10.1088/0957-0233/11/10/311/pdf

A six-electrode local probe for measuring solids velocity and volume fraction profiles in solids-water flows

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

Electrical capacitance tomography (ECT) provides information on the flow regime and concentration distribution in process vessels and pipelines containing two-phase mixtures. This is achieved by arranging sensors around the pipe or vessel to be imaged. The sensor output signals depend on the position of the phases within the sensing zone. A computer is then used to reconstruct an image of the pipe cross section from the sensor measurements. It is necessary to calibrate the ECT system by filling the sensing zone consecutively with the low permittivity material, then the high permittivity material. When the high permittivity material is introduced into a low permittivity background within the sensing zone, the capacitance between sensors will increase. This paper demonstrates that this calibration procedure coupled with the existing image reconstruction software is inappropriate for imaging liquid-liquid dispersions containing low fractions (below 0.3) of water in kerosene. An alternative calibration procedure is proposed which yields substantially improved images.

http://iopscience.iop.org/article/10.1088/0957-0233/9/11/002/pdf

Calibration of capacitance tomography systems for liquid-liquid dispersions

Electrical capacitance tomography offers the opportunity to visualize the contents of a process vessel or pipeline which contains dielectric materials or where the continuous phase is a non-conducting dielectric. This work describes the application of this novel imaging technique to a range of liquid-liquid processes from a laboratory-scale mixing vessel to an industrial-scale liquid-liquid contactor. Single-plane specially-designed sensors containing arrays of either 8 or 12 measurement electrodes, with the same number of driven-guard electrodes, were attached to a bench-scale (diameter—0.15 m) mixer, a bench-scale (diameter—0.10 m) flow column, and a large (diameter—0.6 m) flow column. The capacitance measurements were processed by an image reconstruction algorithm based on linear back-projection to convert the measurements to images of the distribution of dispersed phase across the section of the equipment under investigation. Tomographic images of the distribution of dispersed phase were obtained. These images clearly show the distribution of dispersed phase within the sensing zone of these liquid-liquid systems. The potential application of ECT as a non-intrusive monitor of liquid-liquid systems in industrial-scale contactors is very promising indeed.

R.C. Waterfall

Papers

A six-electrode local probe for measuring solids velocity and volume fraction profiles in solids-water flows

Combustion imaging from electrical impedance measurements

Calibration of capacitance tomography systems for liquid-liquid dispersions

Imaging Immiscible Liquid-Liquid Systems by Capacitance Tomography