Three-dimensional electrical capacitance tomography
In ECT, the fringing field from the edges of the plates is viewed as a source of distortion to the final reconstructed image and is thus mitigated by guard electrodes.
Assuming a static or quasi-static regime and the presence of a lossless dielectric medium, such as a perfect insulator, in the region between the plates, the field obeys the following equation:
This is in contrast to hard-field tomography, such as X-ray CT, where the electric field lines do not change in the presence of a test subject.
Prior to the actual measurements, a calibration and normalization procedure is necessary to cancel out the effects of stray capacitance and any insulating wall between the electrodes and the region of interest to be imaged.
[9] Increasing the electrode size, on the other hand, does not result in non-uniform charge distribution over the plates, which may exacerbate the ill-posedness of the problem.
Reconstruction methods address the inverse problem of 3D ECT imaging, i.e. to determine the volumetric permittivity distribution form the mutual capacitance measurements.
Traditionally, the inverse problem is handled through the linearization of the (nonlinear) relationship between the capacitance and the material permittivity equation using the Born approximation.
Similar to single step methods, these algorithms also use linearized sensitivity matrix for the projections to obtain the permittivity distribution inside the domain.
Projection-based iterative methods typically provide better images than non-iterative algorithms yet require more computational resources.
DCPT utilizes the full admittance information by means of the small angle phase component of this complex valued data.
Advanced measuring techniques are required to monitor and quantify phase hold ups in such multiphase flows.
Due to their relatively fast speed of acquisition and non-intrusive characteristics, 2D and 3D ECT are widely used in industries for flow monitoring.
Knowing that a mixture will exhibit dielectric relaxation due to the MWS effect, this additional measuring dimension can be exploited to decompose multiphase flows when at least one of the phases is conducting.
The use of the sensitivity gradient[11] enables the reconstruction of 3D velocity profiles using an ECT sensor, which can readily provide information of fluid dynamics.
The application of the sensitivity gradient provides significant improvement over more traditional (cross-correlation based) velocimetry, exhibiting better image quality and requiring less computational time.
Another advantage of the sensitivity gradient based velocimetry is its compatibility with conventional image reconstruction algorithms used in 3D ECT.
Compared to other sensing and imaging equipment such as gamma radiation, x-ray, or MRI machines, 3D ECT remains relatively cheap to manufacture and operate.
Part of this quality of the technology is due to its low energy emissions which do not require any additional mechanisms of containing waste or insulating high power outputs.
This can be done by (a) adaptive acquisitions with synthetic electrodes,[10] (b) spatio-temporal sampling using additional measurements obtained when objects are in different positions inside the sensor,[21] (c) multi-frequency operation to exploit permittivity variations with frequency due to the MWS effect,[14] and (d) combining ECT with other sensing modalities, either based on the same hardware (such as DCPT) or on additional hardware (such as microwave tomography).
In the past, 3D ECT has been extensively tested in a wide range of multi-phase flow systems in laboratory as well as industrial settings.
[9] ECT's unique ability to obtain real-time non-invasive spatial visualization of systems with complex geometries under different temperature and pressure conditions at relatively low costs renders it favorable for both fundamental fluid mechanics research and applications in large-scale processing industries.
[24] The flexibility of the 3D ECT sensor geometry also enables it for imaging of bend, tapering and other non-uniform sections of gas-solid flow reactors.
The bubbling flow phenomena have been extensively researched with computational fluid dynamic methods as well as traditional invasive measurement techniques.
ECT possesses the unique ability to obtain real-time quantitative visualization of an entire gas-liquid flow field.
[27][26] 3D ECT is shown to be able to capture the spiral motion of bubble plumes, the structures of large scale liquid vortices and gas holdup distributions.
ECT successfully captures the liquid distribution inside the vessel and the off-centered gas core drifting phenomenon.
The trickle bed reactor (TBR) is a typical three-phase gas-liquid-solid system, and has applications in petroleum, petrochemical, biochemical, electrochemical and water treatment industries.
However, ECT has the potential for high-temperature applications due to its simple and robust design and non-invasive nature, which allows for insulating materials to be imbedded in the sensor for heat-resistance.
Currently the high-temperature 3D ECT technology is under rapid development and research efforts are being made to address engineering issues associated with high temperatures.
Issues such as corroded steel, water penetration, and air voids are often embedded within concrete or other solid members.
