Applications of electrical tomography for gas–solids and liquid–solids flows — a review
Introduction
Tomography offers a unique opportunity to unravel the complexities of the internal structure of an object without the need to invade it. The concept of tomography was first published by a Norwegian physicist Abel [1] for an object with axi-symmetrical geometry. Nearly 100 years later, an Austrian mathematician Radon [2] extended Abel's idea for objects with arbitrary shapes.
The root of the word tomography is derived from the Greek words “tomos” meaning “to slice” and “graph” meaning “image”. The Oxford English Dictionary defines tomography as follows:
Radiography in which an image of a predetermined plane in the body or other object is obtained by rotating the detector and the source of radiation in such a way that points outside the plane give a blurred image. Also in extended use, any analogous technique using other forms of radiation.
The Encyclopaedia Britannica (vol. 11, p. 837) describes tomography in a more application-orientated manner:
A still more complex technique variously called computerised tomography (CT), or computerised axial tomography (CAT), was developed by Godfrey Hounsfield of Great Britain and Allen Cormack of the United States during the 1970s. Since then it has become a widely used diagnostic approach. In this procedure, a narrow beam of X-rays sweeps across an area of the body and is recorded not on film but with a radiation detector as a pattern of electrical impulses. Data from many sweeps are integrated by a computer, which uses the radiation absorption figures to assess the density of tissues at thousands of points. The density values appear on a television-like screen as points of varying brightness to produce a detailed cross-sectional image of the internal structure under scrutiny.
As it can be concluded from this description, tomography is often perceived as an imaging tool for medical examination purposes. It has to be emphasised, however, that the concept of tomography and its noninvasive way of imaging are not restricted to the medical field. Tomography has been developed, over the last decade, into a reliable tool for imaging numerous industrial applications [3], [4], [5]. This field of application is commonly known as industrial process tomography or simply process tomography.
In recent years, the advances in industrial process tomography techniques have been the subjects of many research initiatives and international conferences. In the United Kingdom the Technology Foresight Challenge Project: Process tomography — a new dimension in advanced sensor technology started in 1996. Annual meetings of the European Concerted Action on Process Tomography (ECAPT) were organised in the years 1992–1995 and conferences of the United Engineering Foundation took place in the years 1995 and 1997. In April 1999, the First World Congress on Industrial Process Tomography was held in Buxton, UK.
Currently, there are a number of tomographic techniques, other than electrical methods discussed in this paper, available for studying the complex multiphase phenomena. These include, for example, X-ray, γ-ray and positron emission tomography (PET) systems [6], magnetic resonance imaging (MRI) [7], ultrasonic systems [8], optical [9], [10] and infrared [11] tomography. Each of these techniques has its advantages, disadvantages and limitations. The choice of a particular technique is usually dictated by many, very often contradictory, factors. These include: physical properties of the constituents of multiphase flow, the desired spatial and temporal resolution of imaging, cost of the equipment, its physical dimensions, human resources needed to operate it, and potential hazards to the personnel involved (e.g. radiation).
Electrical tomography is one of the available methods. It is relatively fast (up to 200 images per second) and simple to operate, has a rugged construction and is sufficiently robust to cope with most of the industrial environments. The apparent drawback of electrical tomography is its relatively low spatial resolution — typically 3–10% of a pipe diameter. This however should be viewed in the context of the practical industrial applications.
Electrical tomography can be used to obtain both qualitative and quantitative data needed in modelling a multifluid system. For instance, different flow patterns are characterised, in a qualitative way; by using both time and space scales. Next, a process model verification of a qualitative model is made, based on comparisons between calculated fields of concentration or velocity and measurement results. Here, tomographic data provides, in a noninvasive way, cross-sectional profiles of the distribution of materials or velocities in a process vessel or pipeline. Results obtained from tomographic measurements can then be applied for process design or process control. Electrical tomography is, in certain cases, the most attractive method for real-time imaging of industrial processes, because of its inherent simplicity and high-speed capabilities.
The aim of this paper is to present the fundamentals of electrical tomography and its applications to gas–solids and liquid–solids flows. Examples show flow morphology within pneumatic and hydraulic conveying systems, solids distribution within a fluidised bed and a dipleg, and solids profiles within a hydrocyclone for various operating conditions. The results were obtained using two electrical tomography systems: electrical capacitance tomography (ECT) and electrical resistance (or resistivity) tomography (ERT).
Section snippets
Historical background and general information
The theoretical model, linking the dielectric permittivity (or electrical conductivity) of a two-phase mixture to the volume fraction of one material dispersed within another was first presented by Maxwell [12]. In his calculations Maxwell assumed that small spheres of one material were uniformly distributed in the continuous phase of another material, and that an otherwise homogeneous electrical field is disturbed by their presence. The spheres were assumed to be of equal diameter, and small
Reconstruction algorithms
As can be seen from previous 2.2 Capacitance tomography, 2.3 Resistivity tomography, both capacitance and resistivity tomography are governed by similar partial differential equations , , respectively). Therefore, reconstruction algorithms for both tomographic modalities have many similar features. To focus our attention, ECT systems will be discussed here in more detail.
Some important concepts related to the reconstruction algorithms are those of “forward” and “inverse” problems. The forward
Applications
In this section, tomographic data, obtained for various modes of gas–solids and liquid–solids flows, will be reviewed. the images were captured with speeds between 100 and 200 frames per second. their spatial resolution was about one tenth of a pipe diameter. the results were published by Dyakowski et al. [38], [39], [40], Fangary et al. [41], Loh et al. [42], Mckee et al. [43], Wang et al. [44], and Williams et al. [45]. The examples include gas–solids flow in the riser and the dipleg of a
Conclusions
This paper presents an overview of the electrical tomographic methods, and in particular focuses on their applications for investigating, monitoring and controlling of wet and dry particulate systems.
The unique features of electrical tomography include high speed imaging capabilities (typically between 100 and 200 frames per second), simplicity and robustness. The typical spatial resolution of 3–10% of pipe diameter is sufficient for many research and industrial applications.
The case studies
References (53)
- et al.
Experimental methods in fluidization research
Int. J. Multiphase Flow
(1994) - et al.
Concentration profiles in a gravity chute conveyor by optical tomography measurement
Powder Technol.
(1998) - et al.
The use of capacitance probes in gas fluidised beds
Powder Technol.
(1972) - et al.
The guarded capacitance probe — a tool for the measurement of solids flow patterns in laboratory and industrial fluidised bed combustors
Powder Technol.
(1997) - et al.
The local structure of gas fluidised beds. 1: A statistically based measuring system
Int. J. Multiphase Flow
(1973) - et al.
Application of capacitance tomography to gas–solid flows
Chem. Eng. Sci.
(1997) - et al.
On-line monitoring of dense phase flow using real time dielectric imaging
Powder Technol.
(1999) - et al.
Application of electrical resistance tomography to detect deposition in hydraulic conveying systems
Powder Technol.
(1998) - et al.
Solid flow imaging and attrition studies in a pneumatic conveyor
Powder Technol.
(1995) - et al.
Real time capacitance imaging of bubble formation at the distributor of a fluidised bed
Chem. Eng. J.
(1995)
Using electrical impedance tomography for controlling hydrocyclone underflow discharge
Control Eng. Practice
Real time visualisation and analysis of dense phase powder conveying
Powder Technol.
Simulation of the performance of electrical capacitance tomography for measurement of dense phase pneumatic conveying
Chem. Eng. J.
J. Reine Agnew. Math.
Ber. Saechs. Akad. Wiss.
Imaging Industrial Flows
Tomographic methods for the analysis of flow patterns in steady and transient flow
Nuclear magnetic resonance in chemical engineering: principles and applications
Chem. Eng. Sci.
Development of an ultrasonic tomography system for application in pneumatic conveying
Meas. Sci. Technol.
Further development of a tomographic imaging system using optical fibres for pneumatic conveyors
Meas. Sci. Technol.
Measurement of flame temperature distribution by IR emission computed tomography
Appl. Opt.
On the influence of obstacles in rectangular order upon the properties of a medium
Philos. Mag.
Die theorie des mschkorpers für dir feld der stationaren stromung
Abh. Sach. Ges. Wiss., Math.-Phys.
Theory of Electric Polarisation
Cited by (266)
Electrical resistance tomography image reconstruction based on one-dimensional multi-branch convolutional neural network combined with attention mechanism
2022, Flow Measurement and InstrumentationMathematical concepts for image reconstruction in tomography
2022, Industrial Tomography: Systems and Applications, Second EditionMeasurement and characterization of slurry flow using Electrical Resistance Tomography
2022, Industrial Tomography: Systems and Applications, Second Edition